MEAN CURVATURE FLOW OF SUBMANIFOLDS WITH SMALL TRACELESS SECOND FUNDAMENTAL FORM
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2015, Vol 9, Issue 9
Abstract
Consider a family of smooth immersions F(; t) : Mn Mn+k of submanifolds in Mn+k moving by mean curvature flow = , where is the mean curvature vector for the evolving submanifold. We prove that for any n >-2 and k>-1, the flow starting from a closed submanifold with small L2-norm of the traceless second fundamental form contracts to a round point in finite time, and the corresponding normalized flow converges exponentially in the C-topology, to an n-sphere in some subspace Mn+1 of Mn+k.
Authors and Affiliations
Zhe Zhou, CHUANXI WU, GUANGHAN LI
Keywords
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- EP ID EP651463
- DOI 10.24297/jam.v9i9.2233
- Views 149
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