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Long-time Existence and Convergence of Graphic Mean Curvature Flow in Arbitrary Codimension | | Mu-Tao Wang
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28 Dec 2001 | | Subject: | Differential Geometry; Analysis of PDEs | math.DG math.AP | | Abstract: | Let f:Sigma_1 --> Sigma_2 be a map between compact Riemannian manifolds of constant curvature. This article considers the evolution of the graph of f in the product of Sigma_1 and Sigma_2 by the mean curvature flow. Under suitable conditions on the curvature of Sigma_1 and Sigma_2 and the differential of the initial map, we show that the flow exists smoothly for all time. At each instant t, the flow remains the graph of a map f_t and f_t converges to a constant map as t approaches infinity. This also provides a regularity estimate for Lipschtz initial data. | | Source: | arXiv, math.DG/0112297 | | Services: | Forum | Review | PDF | Favorites | |
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