Frontiers of Mathematics in China >

2009 , Vol. 4 >Issue 2: 283 - 296

DOI: https://doi.org/10.1007/s11464-009-0018-4

RESEARCH ARTICLE

Singularities of symplectic and Lagrangian mean curvature flows

  • Xiaoli HAN 1 ,
  • Jiayu LI , 2,3
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  • 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

Received date: 27 Sep 2008

Accepted date: 13 Feb 2009

Published date: 05 Jun 2009

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

In this paper, we study the singularities of the mean curvature flow from a symplectic surface or from a Lagrangian surface in a Kähler-Einstein surface. We prove that the blow-up flow ∑s∞ at a singular point(X0, T0) of a symplectic mean curvature flow Σt or of a Lagrangian mean curvature flow Σt is a nontrivial minimal surface in ℝ4, if ∑-∞∞ is connected.

Key words： Symplectic surface; holomorphic curve; Lagrangian surface; minimal Lagrangian surface; mean curvature flow

Cite this article

Xiaoli HAN , Jiayu LI . Singularities of symplectic and Lagrangian mean curvature flows[J]. Frontiers of Mathematics in China, 2009 , 4(2) : 283 -296 . DOI: 10.1007/s11464-009-0018-4

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