| ε_0-Regularity for Mean Curvature Flow from Surface to Flat Riemannian Manifold |
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| 基金项目： | The first author is supported by National Natural Science Foundation of China （Grant No. 10901088）Acknowledgements The second author thanks Abdus Salam ICTP for the good work condition. The authors would like to thank Professor Jiayu Li for his helpful discussion. |
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| 摘 要： | In this paper we prove an ε0-regularity theorem for mean curvature flow from surface to a flat Riemannian manifold. More precisely, we prove that if the initial energy ∫Σ0 |A|2 ≤ε0 and the initial area μ0(Σ0) is not large, then along the mean curvature flow, we have ∫Σt|A|2 ≤ε0. As an application, we obtain the long time existence and convergence result of the mean curvature flow.
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| 关 键 词： | ε-Regularity mean curvature flow |
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