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
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
收藏
页码:365 / 375
页数:11
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