THE MEAN CURVATURE FLOW BY PARALLEL HYPERSURFACES

被引：6

作者：

Santos dos Reis, Hiuri Fellipe ^{[1
]}

Tenenblat, Keti ^{[1
]}

机构：

[1] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 11期

关键词：

Isoparametric hypersurface; mean curvature flow; parallel hypersurface; space forms; ISOPARAMETRIC HYPERSURFACES; PRINCIPAL CURVATURES;

D O I：

10.1090/proc/14178

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that a hypersurface of a space form is the initial data for a solution to the mean curvature flow by parallel hypersurfaces if and only if it is isoparametric. By solving an ordinary differential equation, explicit solutions are given for all isoparametric hypersurfaces of space forms. In particular, for such hypersurfaces of the sphere, the exact collapsing time into a focal submanifold is given in terms of its dimension, the principal curvatures, and their multiplicities.

引用

页码：4867 / 4878

页数：12

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