SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

doi:10.1016/S0252-9602(12)60203-3

Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (1): 171-186.doi: 10.1016/S0252-9602(12)60203-3

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SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

WU Jia-Yong

Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China

Received:2011-09-19 Online:2013-01-20 Published:2013-01-20
Supported by:
This work is partially supported by the NSFC (11101267, 11271132), the Innovation Program of Shanghai Municipal Education Commission (13YZ087), and the Science and Technology Program of Shanghai Maritime University (20120061).

Abstract

Abstract:

Given a family of smooth immersions of closed hypersurfaces in a locally sym-metric Riemannian manifold with bounded geometry, moving by mean curvature flow, we show that at the first finite singular time of mean curvature flow, certain subcritical quan-tities concerning the second fundamental form blow up. This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of Le in the Euclidean case.

Key words: mean curvature flow, Riemannian submanifold, integral curvature, maximal existence time

CLC Number:

53C40

WU Jia-Yong. SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS[J].Acta mathematica scientia,Series B, 2013, 33(1): 171-186.

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SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

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