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Evolution of hypersurfaces by the mean curvature minus an external force field 被引量:11
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作者 Yan-nan LIU Huai-yu JIAN 《Science China Mathematics》 SCIE 2007年第2期231-239,共9页
In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is... In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force. 展开更多
关键词 parabolic equation mean curvature flow maximum principle (for tensor) 35K45 53a05
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A curve flow evolved by a fourth order parabolic equation 被引量:6
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作者 LIU YanNan JIAN HuaiYu 《Science China Mathematics》 SCIE 2009年第10期2177-2184,共8页
We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ?2, the flow has a smooth solution fo... We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ?2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional. 展开更多
关键词 geometric evolution equations fourth order energy estimate 35J60 35K45 52K44 53a05
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Mechanical theorem proving in the surfaces using the characteristic set method and Wronskian determinant 被引量:1
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作者 FENG RuYong YU JianPing 《Science China Mathematics》 SCIE 2008年第10期1763-1774,共12页
In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian deter... In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian determinant, which can be used to decide whether the elements in a partial differential field are linearly dependent over its constant field. Based on Wronskian determinant, we can describe the geometry statements in the surfaces by an algebraic language and then prove them by the characteristic set method. 展开更多
关键词 mechanical theorem proving Wu-Ritt’s characteristic set method local theory of surface Wronskian determinant 12H99 53a05
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