Mean curvature Flow with convex Gauss image

Details Mean curvature Flow with convex Gauss image Mean curvature Flow with convex Gauss image

2005-12-15

arxiv.org/abs/math/0512380v1

Mathematics

Differential Geometry

36 pages

Scientific paper

We study the mean curvature flow of complete space-like submanifolds in pseudo-Euclidean space with bounded Gauss image, as well as that of complete submanifolds in Euclidean space with convex Gauss image. By using the confinable property of the Gauss image under the mean curvature flow we prove the long time existence results in both cases. We also study the asymptotic behavior of these solutions when $t\to\infty$.

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