CONTRACTION OF CONVEX HYPERSURFACES IN EUCLIDEAN-SPACE

被引：213

作者：

ANDREWS, B ^{[1
]}

机构：

[1] AUSTRALIAN NATL UNIV,CTR MATH & APPLICAT,CANBERRA,ACT 2601,AUSTRALIA

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 1994年 / 2卷 / 02期

关键词：

D O I：

10.1007/BF01191340

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of fully nonlinear parabolic evolution equations for hypersurfaces in Euclidean space. A new geometrical lemma is used to prove that any strictly convex compact initial hypersurface contracts to a point in finite time, becoming spherical in shape as the limit is approached. In the particular case of the mean curvature flow this provides a simple new proof of a theorem of Huisken.

引用

页码：151 / 171

页数：21

共 19 条

[1]

ANDREWS B, 1992, MR2192 CMA AUSTR NAT

[2]

ANDREWS B, IN PRESS J DIFFER GE

[3] NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .5. THE DIRICHLET PROBLEM FOR WEINGARTEN HYPERSURFACES [J].