Examples of hypersurfaces flowing by curvature in a Riemannian manifold

被引：0

作者：

Gulliver, Robert ^{[1
]}

Xu, Guoyi ^{[1
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2009年 / 17卷 / 04期

关键词：

CONVEX HYPERSURFACES; CONTRACTION;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper gives some examples of hypersurfaces phi(t)(M-n) evolving in time with speed determined by functions of the normal curvatures in an (n + 1)-dimensional hyperbolic manifold; we emphasize the case of flow by harmonic mean curvature. The examples converge to a totally geodesic submanifold of any dimension from 1 to n, and include cases which exist for infinite time. Convergence to a point was studied by Andrews, and only occurs in finite time. For dimension n = 2, the destiny of any harmonic mean curvature flow is strongly influenced by the genus of the surface M-2.

引用

页码：701 / 719

页数：19

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