Mean curvature flow with convex Gauss image

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.