Chinese Annals of Mathematics, Series B

, Volume 29, Issue 2, pp 121–134

Mean curvature flow with convex Gauss image

Article

DOI: 10.1007/s11401-007-0212-1

Cite this article as:
Xin, Y. Chin. Ann. Math. Ser. B (2008) 29: 121. doi:10.1007/s11401-007-0212-1

Abstract

In this paper, the mean curvature flow of complete submanifolds in Euclidean space with convex Gauss image and bounded curvature is studied. The confinable property of the Gauss image under the mean curvature flow is proved, which in turn helps one to obtain the curvature estimates. Then the author proves a long time existence result. The asymptotic behavior of these solutions when t → ∞ is also studied.

Keywords

Mean curvature flow Convex Gauss image Curvature estimates Long time existence 

2000 MR Subject Classification

53C44 

Copyright information

© Editorial Office of CAM (Fudan University) and Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical SciencesFudan UniversityShanghaiChina

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