Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (4): 1053-1064.doi: 10.1016/S0252-9602(10)60102-6

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A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

 CHEN Xu-Zhong, SHEN Yi-Bing**   

  1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China
  • Received:2006-12-29 Revised:2008-09-30 Online:2010-07-20 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)

Abstract:

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

CLC Number: 

  • 53C44
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