紧凸超曲面在一类带外力场的平均曲率流下的收缩

CONTRACTION OF CONVEX HYPERSURFACES BY THEIR MEAN CURVATURE MINUS A KIND OF EXTERNAL FORCE FIELD

在文献[1]中作者们证明了,若外力场函数是某类线性函数时,带外力场的平均曲率流短时间存在,且保持凸性.在此基础上证明了若初始曲面是严格凸紧超曲面时,曲面在有限时间内收缩为一点.

In [ 1 ] , the authors proved that if external force field is a kind of linear fucntions, the mean curvature flow with external force field smoothly exists in a finite time interval and the convexity of the hypersurfaces is preserved. Based on these results, we will prove that if the initial hypersurface is srictly convex and compact, it will contract to a point in finite time.