The second type singularity of symplectic and Lagrangian mean curvature flows

TL;DR

This paper investigates type II singularities in symplectic and Lagrangian mean curvature flows within Kähler-Einstein surfaces, revealing a relationship between the Kähler angle and the mean curvature in the limit flow.

Contribution

It establishes a connection between the maximum Kähler angle and the maximum mean curvature squared during the flow's singularity formation.

Findings

Relation between Kähler angle and mean curvature at singularities

Characterization of type II singularities in symplectic and Lagrangian flows

Insights into the behavior of the flow near singularities

Abstract

In this paper we mainly study the type II singularities of the mean curvature flow from a symplectic surface or from an almost calibrated Lagrangian surface in a K \"ahler-Einstein surface. We show the relation between the maximum of the K\"ahler angle and the maximum of $|H|^2$ on the limit flow.