广义各向异性流的凸性定理

A Convexity Theorem for a Type of Generalized Anisotropic Flow

曲线流不仅可用于解决曲面上闭测地线的存在性等几何问题,而且可作为相变理论中描述界面运动的物理模型。论文对一类描述界面运动的各向异性流进行了细致分析,推广了-δwh isker引理,并利用b low-up技巧证明了界面在退化成一点之前必先变为凸曲线。

Curve shortening flow is not only used to study differential geometric problems such as the existence of closed geodesies on surfaees, but also served as the physical model describing the motion of interface in the theory of phase transition. A type of anisotropic flow describing the motion of interface is investigated. The δ-whisker lemma is generalized. Also it is proved that the interface becomes convex before shrinking to a point.