CURVATURE CONTRACTION FLOWS IN THE SPHERE

被引：7

作者：

McCoy, James A. ^{[1
]}

机构：

[1] Univ Wollongong, Inst Math & Its Applicat, North Fields Ave, Wollongong, NSW 2522, Australia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Curvature flow; parabolic partial differential equation; hypersurface; axial symmetry; spherical geometry; ALEXANDROV-FENCHEL TYPE; CONVEX HYPERSURFACES; MEAN-CURVATURE; INEQUALITIES; SURFACES;

D O I：

10.1090/proc/13831

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that convex surfaces in an ambient three-sphere contract to round points in finite time under fully nonlinear, degree one homogeneous curvature flows, with no concavity condition on the speed. The result extends to convex axially symmetric hypersurfaces of Sn+1. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature.

引用

页码：1243 / 1256

页数：14

共 42 条

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