双曲空间中的紧致超曲面在平均曲率下的形变

Deforming Compact Hypersurfaces in a Hyperbolic Space by Their Mean Curvature

本文考虑双曲空间中的紧致超曲面在平均曲率下的形变．证明了如果初始曲面满足某一凸性条件，则超曲面收敛到一个“圆点”．

In this paper, the deformation of compact hypersurfaces in a hyperbolic space by their mean curvatures is considered. It is proved that such deforming hypersurfaces converge to a round point in Huiskens sense, provided that the initial hypersurface satisfies a certain convexity condition.