Hyperbolic mean curvature flow |
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Authors: | Chun-Lei He Kefeng Liu |
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Institution: | a Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China b Department of Mathematics, Zhejiang University, Hangzhou 310027, China c Department of Mathematics, University of California at Los Angeles, CA 90095, USA |
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Abstract: | In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations is strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive nonlinear wave equations satisfied by some geometric quantities related to the hyperbolic mean curvature flow. Moreover, we also discuss the relation between the equations for hyperbolic mean curvature flow and the equations for extremal surfaces in the Minkowski space-time. |
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Keywords: | 58J45 58J47 |
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