Flow by mean curvature of convex surfaces into spheres
Flow by mean curvature of convex surfaces into spheres
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DOI：
10.4310/jdg/1214438998
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发表时间：
1984
影响因子：
2.5
通讯作者：
G. Huisken
中科院分区：
文献类型：
--
作者：
G. Huisken
Brakke [1]从几何测度论的观点研究了曲面按平均曲率运动的问题。其他作者研究了相应的非参数问题[2]，[5]，[9]。这种兴趣的一个原因是，规定的平均曲率的演变表面模型的行为，在退火纯金属晶界。本文采用一种更经典的观点：考虑光滑嵌入R中的紧致一致凸无边界的w维曲面M = Mo。设Mo局部地用一个自同态表示
The motion of surfaces by their mean curvature has been studied by Brakke [1] from the viewpoint of geometric measure theory. Other authors investigated the corresponding nonparametric problem [2], [5], [9]. A reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal. In this paper we take a more classical point of view: Consider a compact, uniformly convex w-dimensional surface M = Mo without boundary, which is smoothly imbedded in R. Let Mo be represented locally by a diffeomorphism