Evolving Compact Locally Convex Curves and Convex Hypersurfaces

被引：1

作者：

Gao, Laiyuan ^{[1
]}

Zhang, Yuntao ^{[1
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, 101 Shanghai Rd, Xuzhou, Jiangsu, Peoples R China

来源：

MANUSCRIPTA MATHEMATICA | 2022年 / 167卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

GAUSS CURVATURE FLOW; MEAN-CURVATURE; CLOSED CURVES; EVOLUTION; SINGULARITIES; SURFACES;

D O I：

10.1007/s00229-021-01278-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A nonlocal curvature flowis investigated to evolve compact locally convex hypersurfaces in the Euclidean space En+1. It is shown that the flow exists globally in all dimensions and deforms the evolving curve into an m-fold circle in the plane if n = 1 and drives the evolving hypersurface into a Euclidean sphere if n > 1.

引用

页码：365 / 375

页数：11

共 27 条

[1]

ABRESCH U, 1986, J DIFFER GEOM, V23, P175

[2] Gauss curvature flow: the fate of the rolling stones [J].