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

作　　者：刘艳楠[1] 

机构地区：[1]北京工商大学计算机与信息工程学院,北京100048

出　　处：《北京工商大学学报（自然科学版）》2010年第4期73-77,共5页Journal of Beijing Technology and Business University:Natural Science Edition

基　　金：北京市属高校科技创新平台资助项目(201098)

摘　　要：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.

关 键 词：抛物方程 平均曲率流 张量的极值原理 

分 类 号：O175.25[理学—数学] O186.12[理学—基础数学]