Singularities of symplectic and Lagrangian mean curvature flows

Details Singularities of symplectic and Lagrangian mean curvature flows Singularities of symplectic and Lagrangian mean curvature flows

2006-11-28

arxiv.org/abs/math/0611857v4

Mathematics

Differential Geometry

Scientific paper

In this paper we study the singularities of the mean curvature flow from a symplectic surface or from a Lagrangian surface in a K\"ahler-Einstein surface. We prove that the blow-up flow $\Sigma_s^\infty$ at a singular point $(X_0, T_0)$ of a symplectic mean curvature flow $\Sigma_t$ or of a Lagrangian mean curvature flow $\Sigma_t$ is a non trivial minimal surface in ${\bf R}^4$, if $\Sigma_{-\infty}^\infty$ is connected.

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