Tangent Flows of Symplectic Mean Curvature Flows

Abstract

We prove that the tangent cone at the first blow-up time of the mean curvature flow of a closed symplectic surface in a compact Kähler-Einstein surface consists of a finite union of planes in $\mathbf{R}^4$. Furthermore, when the flow develops a Type I* singularity at $(X_0,T)$, then the tangent cone is a holomorphic cone.