We review the (2 + 1)-dimensional Baňados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3 + 1)-dimensional spacetime. For the matter content we use a scalar-gauge field. The me...We review the (2 + 1)-dimensional Baňados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3 + 1)-dimensional spacetime. For the matter content we use a scalar-gauge field. The metric is written as <img src="Edit_be2cdfd9-fda6-4846-b64d-4d1062f9964e.bmp" alt="" /> where the <em>dilaton</em> field <span style="white-space:nowrap;"><span style="white-space:nowrap;">ω</span></span> contains all the scale dependencies and where <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" /> represents the “un-physical” spacetime. A numerical solution is presented and shows how the dilaton can be treated on equal footing with the scalar field. The location of the apparent horizon and ergo-surface depends critically on the parameters and initial values of the model. It is not a hard task to find suitable initial parameters in order to obtain a regular and singular free <img src="Edit_5d830100-019b-4a6a-82e7-deefdf327ecc.bmp" alt="" /> out of a BTZ-type solution for <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" style="white-space:normal;" />. In the vacuum situation, an exact time-dependent solution in the Eddington-Finkelstein coordinates is found, which is valid for the (2 + 1)-dimensional BTZ spacetime as well as for the uplifted (3 + 1)-dimensional BTZ spacetime. While <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" style="white-space:normal;" /> resembles the standard BTZ solution with its horizons, <img src="Edit_5d830100-019b-4a6a-82e7-deefdf327ecc.bmp" alt="" style="white-space:normal;" /> is flat. The dilaton field becomes an infinitesimal renormalizable quantum field, which switches on and off Hawking radiation. This solution can be used to investigate the small distance scale of the model and the black hole complementarity issues. It can also be used to describe the problem of how to map the quantum states of the outgoing radiation as seen by a distant observer and the ingoing by a local observer in a one-to-one way. The two observers will use a different conformal gauge. A possible connection is made with the antipodal identification and unitarity issues. This research shows the power of conformally invariant gravity and can be applied to bridge the gap between general relativity and quantum field theory in the vicinity of the horizons of black holes.展开更多
We study a prescribing involving Poisson kernel on the unit of PDE. As in Nirenberg problem, solutions. We prove existence in the functions problem of a conformally invariant integral equation ball. This integral equa...We study a prescribing involving Poisson kernel on the unit of PDE. As in Nirenberg problem, solutions. We prove existence in the functions problem of a conformally invariant integral equation ball. This integral equation is not the dual of any standard type there exists a Kazdan-Warner type obstruction to existence of antipodal symmetry functions class.展开更多
The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, ...The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.展开更多
We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-e...We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity.展开更多
In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff E...In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff Equations, and two examples are presented to illustrate the application of the results.展开更多
In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultan...In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.展开更多
This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differenti...This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.展开更多
This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are g...This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.展开更多
This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the c...This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.展开更多
This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigati...This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.展开更多
This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding confor...This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.展开更多
This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infini...This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.展开更多
In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is gi...In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.展开更多
We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation v...We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.展开更多
In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinite...In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system＇s conformal invariance and Mei symmetry are discussed. And Appell system＇s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.展开更多
This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conf...This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invaxiance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.展开更多
Conformal invariance and a kind of Hojman conserved quantity of the Nambu system under infinitesimal transformations are studied. The definition and the determining equation of conformal invariance of the system are p...Conformal invariance and a kind of Hojman conserved quantity of the Nambu system under infinitesimal transformations are studied. The definition and the determining equation of conformal invariance of the system are presented. The necessary and sufficient condition under which the conformal invariance of the system would have Lie symmetry under infinitesimal transformations is derived. Then, the condition of existence and a kind of Hojman conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.展开更多
Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with varia...Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal oneparameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.展开更多
In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form △2ψ ＋ L（x,△ ψ）, including the ...In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form △2ψ ＋ L（x,△ ψ）, including the conformal hessian operator.展开更多
文摘We review the (2 + 1)-dimensional Baňados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3 + 1)-dimensional spacetime. For the matter content we use a scalar-gauge field. The metric is written as <img src="Edit_be2cdfd9-fda6-4846-b64d-4d1062f9964e.bmp" alt="" /> where the <em>dilaton</em> field <span style="white-space:nowrap;"><span style="white-space:nowrap;">ω</span></span> contains all the scale dependencies and where <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" /> represents the “un-physical” spacetime. A numerical solution is presented and shows how the dilaton can be treated on equal footing with the scalar field. The location of the apparent horizon and ergo-surface depends critically on the parameters and initial values of the model. It is not a hard task to find suitable initial parameters in order to obtain a regular and singular free <img src="Edit_5d830100-019b-4a6a-82e7-deefdf327ecc.bmp" alt="" /> out of a BTZ-type solution for <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" style="white-space:normal;" />. In the vacuum situation, an exact time-dependent solution in the Eddington-Finkelstein coordinates is found, which is valid for the (2 + 1)-dimensional BTZ spacetime as well as for the uplifted (3 + 1)-dimensional BTZ spacetime. While <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" style="white-space:normal;" /> resembles the standard BTZ solution with its horizons, <img src="Edit_5d830100-019b-4a6a-82e7-deefdf327ecc.bmp" alt="" style="white-space:normal;" /> is flat. The dilaton field becomes an infinitesimal renormalizable quantum field, which switches on and off Hawking radiation. This solution can be used to investigate the small distance scale of the model and the black hole complementarity issues. It can also be used to describe the problem of how to map the quantum states of the outgoing radiation as seen by a distant observer and the ingoing by a local observer in a one-to-one way. The two observers will use a different conformal gauge. A possible connection is made with the antipodal identification and unitarity issues. This research shows the power of conformally invariant gravity and can be applied to bridge the gap between general relativity and quantum field theory in the vicinity of the horizons of black holes.
基金Supported in part by NSFC(Grant Nos.11501034 and 11571019)a key project of NSFC(Grant No.11631002)
文摘We study a prescribing involving Poisson kernel on the unit of PDE. As in Nirenberg problem, solutions. We prove existence in the functions problem of a conformally invariant integral equation ball. This integral equation is not the dual of any standard type there exists a Kazdan-Warner type obstruction to existence of antipodal symmetry functions class.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604036 and State Key Laboratory of 0il/Gas Reservoir Geology and Exploitation ＂PLN0402＂ The authors would like to thank Prof. Sen-Yue Lou for his help and discussion.
文摘The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.
基金the National Natural Science Foundation of China(Grant No.11771099)supported by the Hong Kong Research Grant Council(Grant Nos.PolyU 15302114,15300715,15301716,15300717)supported by the Innovation Program of Shanghai Municipal Education Commission。
文摘We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity.
基金the National Natural Science Foundation of China(10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education,China(20040007022)
文摘In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff Equations, and two examples are presented to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10372053,10572021 and 10772025)the National Natural Science Foundation of Henan province of China(Grant No 0311010900)
文摘In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.
基金supported by the National Natural Science Foundation of China (Grant No 10372053)the Natural Science Foundation of Henan Province,China (Grant Nos 082300410330 and 082300410370)
文摘This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.
基金Supported by National Natural Science Foundation of China under Grant No. 10972151the Natural Science Foundation of Higher Education Institution of Jiangsu Province under Grant No. 08KJB130002
文摘This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant No10772025)the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China (Grant No 08KJB130002)
文摘This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10472040, 10572021 and 10772025)the Outstanding Young Talents Training Found of Liaoning Province of China (Grant No 3040005)
文摘This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.
文摘In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos.10672143 and 60575055)
文摘We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.
基金supported by the National Natural Science Foundation of China (Grant Nos.10672143 and 60575055)
文摘In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system＇s conformal invariance and Mei symmetry are discussed. And Appell system＇s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.
基金Project supported by the Graduate Students Innovative Foundation of China University of Petroleum (East China) (Grant NoS2009-19)
文摘This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invaxiance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No. 09CX04018A)
文摘Conformal invariance and a kind of Hojman conserved quantity of the Nambu system under infinitesimal transformations are studied. The definition and the determining equation of conformal invariance of the system are presented. The necessary and sufficient condition under which the conformal invariance of the system would have Lie symmetry under infinitesimal transformations is derived. Then, the condition of existence and a kind of Hojman conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.
基金Project supported by the Key Disciplines’ Building Foundation of Henan Institute of Educationthe Natural Science Foundation of Education Bureau of Henan Province,China (Grant No. 2009A140003)the Young Core Instructor from Henan Institute of Education
文摘Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal oneparameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.
基金partially supported by NSF grant DMS-1501004partially supported by NSFC(11701027)
文摘In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form △2ψ ＋ L（x,△ ψ）, including the conformal hessian operator.
