Let/(z) be a holomorph.self-map on C.-G-(0) with essential singularities 0 and It is proved that f(z) has a completdy invariant domain.D.F(f),then D is doubly connected and D contains all the singularities of the inv...Let/(z) be a holomorph.self-map on C.-G-(0) with essential singularities 0 and It is proved that f(z) has a completdy invariant domain.D.F(f),then D is doubly connected and D contains all the singularities of the inverse of f(z),moreover,if f is of the finite type, then D=F(f). This result implies that f(z) has at most one completely invariant domain in F(f).展开更多
In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not pre...In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.展开更多
Abstract This paper gencralizes the result about linear isometries of S~ spaces given by W.P.Novinger and D.M.Oberlin[2]for the unite dise of C to the bounded symmetric domains of C^n
In terms of Caratheodory metric and Kobayashi metric, distortion theorems for biholomorphic convex mappings on bounded circular convex domains are given.
The estimations of the bounds of the Bloch constant of locally biholomorphic mappingson irreducible bounded symmetric domains are given. When the domain is a unit circle, theestimation of the lower bounds is just the ...The estimations of the bounds of the Bloch constant of locally biholomorphic mappingson irreducible bounded symmetric domains are given. When the domain is a unit circle, theestimation of the lower bounds is just the famous one-half estimation.展开更多
The distortion theorem for biholomorphic staxlike mappings(with respect to origin) inbounded symmetric domains are given.The distortion theorem for locally biholomorphic convexmappings in bounded symmetric domains are...The distortion theorem for biholomorphic staxlike mappings(with respect to origin) inbounded symmetric domains are given.The distortion theorem for locally biholomorphic convexmappings in bounded symmetric domains are given also.展开更多
The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D C, all of whose zeros have multiplicity at least k, where k ≥...The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D C, all of whose zeros have multiplicity at least k, where k ≥ 2 is an integer. Let h（z） ≠ 0 and oo be a meromorphic function on D. Assume that the following two conditions hold for every f C Dr ： （a） f（z） = 0 =→ ｜f（k）（z）｜ 〈｜h（z）｜. （b） f（k）（z） ≠ h（z）. Then F is normal on D.展开更多
The author,motivated by his results on Hermitian metric rigidity,conjectured in [4] that a proper holomorphic mapping f：Ω→Ω′from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domai...The author,motivated by his results on Hermitian metric rigidity,conjectured in [4] that a proper holomorphic mapping f：Ω→Ω′from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ′is necessarily totally geodesic provided that r′：=rank（Ω′）≤rank（Ω）：=r.The Conjecture was resolved in the affirmative by I.-H.Tsai [8].When the hypothesis r′≤r is removed,the structure of proper holomorphic maps f：Ω→Ω′is far from being understood,and the complexity in studying such maps depends very much on the difference r′-r,which is called the rank defect.The only known nontrivial non-equidimensional structure theorems on proper holomorphic maps are due to Z.-H.Tu [10],in which a rigidity theorem was proven for certain pairs of classical domains of type I,which implies nonexistence theorems for other pairs of such domains.For both results the rank defect is equal to 1,and a generaliza- tion of the rigidity result to cases of higher rank defects along the line of arguments of [10] has so far been inaccessible. In this article, the author produces nonexistence results for infinite series of pairs of （Ω→Ω′） of irreducible bounded symmetric domains of type I in which the rank defect is an arbitrarily prescribed positive integer. Such nonexistence results are obtained by exploiting the geometry of characteristic symmetric subspaces as introduced by N. Mok and L-H Tsai [6] and more generally invariantly geodesic subspaces as formalized in [8]. Our nonexistence results motivate the formulation of questions on proper holomorphic maps in the non-equirank case.展开更多
In this paper, Schwarz-Pick estimates for high order FrSchet derivatives of holo- morphic self-mappings on classical domains are presented. Moreover, the obtained result can deduce the early work on Sc：hwarz-Pick est...In this paper, Schwarz-Pick estimates for high order FrSchet derivatives of holo- morphic self-mappings on classical domains are presented. Moreover, the obtained result can deduce the early work on Sc：hwarz-Pick estimates of higher-order partial derivatives for bounded holomorphic functions on classical domains.展开更多
This paper shows that the 8-problem for holomorphic (0, 2)-forms on Hubert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation...This paper shows that the 8-problem for holomorphic (0, 2)-forms on Hubert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation for holomorphic (0, 2)-forms on pseudoconvex domains in D.F.N. spaces.展开更多
文摘Let/(z) be a holomorph.self-map on C.-G-(0) with essential singularities 0 and It is proved that f(z) has a completdy invariant domain.D.F(f),then D is doubly connected and D contains all the singularities of the inverse of f(z),moreover,if f is of the finite type, then D=F(f). This result implies that f(z) has at most one completely invariant domain in F(f).
文摘In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.
文摘Abstract This paper gencralizes the result about linear isometries of S~ spaces given by W.P.Novinger and D.M.Oberlin[2]for the unite dise of C to the bounded symmetric domains of C^n
文摘In terms of Caratheodory metric and Kobayashi metric, distortion theorems for biholomorphic convex mappings on bounded circular convex domains are given.
文摘The estimations of the bounds of the Bloch constant of locally biholomorphic mappingson irreducible bounded symmetric domains are given. When the domain is a unit circle, theestimation of the lower bounds is just the famous one-half estimation.
文摘The distortion theorem for biholomorphic staxlike mappings(with respect to origin) inbounded symmetric domains are given.The distortion theorem for locally biholomorphic convexmappings in bounded symmetric domains are given also.
基金Project supported by the National Natural Science Foundation of China(No.11071074)the Outstanding Youth Foundation of Shanghai(No.slg10015)
文摘The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D C, all of whose zeros have multiplicity at least k, where k ≥ 2 is an integer. Let h（z） ≠ 0 and oo be a meromorphic function on D. Assume that the following two conditions hold for every f C Dr ： （a） f（z） = 0 =→ ｜f（k）（z）｜ 〈｜h（z）｜. （b） f（k）（z） ≠ h（z）. Then F is normal on D.
基金a CERG of the Research Grants Council of Hong Kong,China.
文摘The author,motivated by his results on Hermitian metric rigidity,conjectured in [4] that a proper holomorphic mapping f：Ω→Ω′from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ′is necessarily totally geodesic provided that r′：=rank（Ω′）≤rank（Ω）：=r.The Conjecture was resolved in the affirmative by I.-H.Tsai [8].When the hypothesis r′≤r is removed,the structure of proper holomorphic maps f：Ω→Ω′is far from being understood,and the complexity in studying such maps depends very much on the difference r′-r,which is called the rank defect.The only known nontrivial non-equidimensional structure theorems on proper holomorphic maps are due to Z.-H.Tu [10],in which a rigidity theorem was proven for certain pairs of classical domains of type I,which implies nonexistence theorems for other pairs of such domains.For both results the rank defect is equal to 1,and a generaliza- tion of the rigidity result to cases of higher rank defects along the line of arguments of [10] has so far been inaccessible. In this article, the author produces nonexistence results for infinite series of pairs of （Ω→Ω′） of irreducible bounded symmetric domains of type I in which the rank defect is an arbitrarily prescribed positive integer. Such nonexistence results are obtained by exploiting the geometry of characteristic symmetric subspaces as introduced by N. Mok and L-H Tsai [6] and more generally invariantly geodesic subspaces as formalized in [8]. Our nonexistence results motivate the formulation of questions on proper holomorphic maps in the non-equirank case.
基金supported by the National Natural Science Foundation of China (Nos. 11171255, 11101373)the Doctoral Program Foundation of the Ministry of Education of China (No. 20090072110053)+1 种基金the Zhejiang Provincial Natural Science Foundation of China (No. Y6100007)the Zhejiang Innovation Project (No. T200905)
文摘In this paper, Schwarz-Pick estimates for high order FrSchet derivatives of holo- morphic self-mappings on classical domains are presented. Moreover, the obtained result can deduce the early work on Sc：hwarz-Pick estimates of higher-order partial derivatives for bounded holomorphic functions on classical domains.
基金The first author was supported by KOSEF postdoctoral fellowship 1998 and the second author was supported by the Brain Korea 21 P
文摘This paper shows that the 8-problem for holomorphic (0, 2)-forms on Hubert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation for holomorphic (0, 2)-forms on pseudoconvex domains in D.F.N. spaces.
