Acta mathematica scientia, Series B >
A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS
Received date: 2006-12-29
Revised date: 2008-09-30
Online published: 2010-07-20
Supported by
Project supported partially by the National Natural Science Foundation of China (10871171) and the Chinese-Hungarian Sci. and Tech. cooperation (for 2007-2009)
Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in [5]. These a-priori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with
nonnegative sectional curvature.
Key words： Mean curvature flow; singularity; hypersurface; weakly convexity
CHEN Xu-Zhong , SHEN Yi-Bing . A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS[J]. Acta mathematica scientia, Series B, 2010 , 30(4) : 1053 -1064 . DOI: 10.1016/S0252-9602(10)60102-6
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