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Singularities of symplectic and Lagrangian mean curvature flows
Authors:Xiaoli Han  Jiayu Li
Institution:1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; 2. Mathematics Group, The Abdus Salam ICTP, Trieste 34100, Italy; 3. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Abstract:In this paper, we study the singularities of the mean curvature ?ow from a symplectic surface or from a Lagrangian surface in a K?hler-Einstein surface. We prove that the blow-up ?ow s at a singular point(X0, T0) of a symplectic mean curvature ?ow Σt or of a Lagrangian mean curvature ?ow Σt is a nontrivial minimal surface in ?4, if - is connected.
Keywords:Symplectic surface  holomorphic curve  Lagrangian surface  minimal Lagrangian surface  mean curvature flow
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