Curvature flow in hyperbolic spaces

被引：12

作者：

Andrews, Ben ^{[1
,2
]}

Chen, Xuzhong ^{[3
]}

机构：

[1] Tsinghua Univ, Ctr Math Sci, Beijing, Peoples R China

[2] Australia Natl Univ, Inst Math Sci, Canberra, ACT, Australia

[3] East China Normal Univ, Dept Math, Shanghai, Peoples R China

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2017年 / 729卷

基金：

中国国家自然科学基金; 澳大利亚研究理事会;

关键词：

DEFORMING CONVEX HYPERSURFACES; MEAN-CURVATURE; GAUSS CURVATURE; SCALAR CURVATURE; SURFACES; POWERS; CONTRACTION; SPHERES; ROOT;

D O I：

10.1515/crelle-2014-0121

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the evolution of compact convex hypersurfaces in hyperbolic space Hn+1, with normal speed governed by the curvature. We concentrate mostly on the case of surfaces, and show that under a large class of natural flows, any compact initial surface with Gauss curvature greater than 1 produces a solution which converges to a point in finite time, and becomes spherical as the final time is approached. We also consider the higher-dimensional case, and show that under the mean curvature flow a similar result holds if the initial hypersurface is compact with positive Ricci curvature.

引用

页码：29 / 49

页数：21

共 29 条

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