Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University,Shanghai 200433, China
Abstract:
In this paper, the mean curvature flow of complete submanifolds in Euclideanspace 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.