Mean Curvature Flow via Convex Functions on Grassmannian Manifolds |
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Authors: | Yuanlong XIN and Ling YANG |
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Institution: | 1. Institute of Mathematics,Fudan University,Shanghai 200433,China 2. Max Planck Institute for the Mathematics in Sciences,Inselstr.22-24,Leibzig 04103,Germany |
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Abstract: | Using the convex functions on Grassmannian manifolds,the authors obtain the interior estimates for the mean curvature flow of higher codimension.Confinable properties of Gauss images under the mean curvature flow have been obtained,which reveal that if the Gauss image of the initial submanifold is contained in a certain sublevel set of the v-function,then all the Gauss images of the submanifoids under the mean curvature flow are also contained in the same sublevel set of the v-function. Under such restrictions.curvature estimates in terms of v-function composed with the Gauss map can be carried out. |
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Keywords: | Mean curvature flow Convex function Gauss map |
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