MEAN CURVATURE FLOW OF PINCHED SUBMANIFOLDS TO SPHERES

被引：3

作者：

Andrews, Ben ^{[1
]}

Baker, Charles ^{[1
]}

机构：

[1] Australian Natl Univ, Inst Math Sci, Canberra, ACT 0200, Australia

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2010年 / 85卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

ARBITRARY CODIMENSION; LAGRANGIAN SUBMANIFOLDS; MINIMAL SUBMANIFOLDS; CONVEX SURFACES; SPACE-FORMS; HYPERSURFACES; SINGULARITIES; MAPS; CONVERGENCE; MANIFOLDS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider compact submanifolds of dimension n >= 2 in R(n+k), with nonzero mean curvature vector everywhere, and such that the full norm of the second fundamental form is bounded by a fixed multiple (depending on n) of the length of the mean curvature vector at every point. We prove that the mean curvature flow deforms such a submanifold to a point in finite time, and that the solution is asymptotic to a shrinking sphere in some (n + 1)-dimensional affine subspace of R(n+k).

引用

页码：357 / 395

页数：39

共 41 条

[1] HYPERSURFACES WITH CONSTANT MEAN-CURVATURE IN SPHERES [J].