Type II Singularities of Lagrangian Mean Curvature Flow with Zero Maslov Class

TL;DR

This paper proves rigidity theorems for Type II singularities in Lagrangian mean curvature flow with zero Maslov class, extending results from two dimensions to higher dimensions, especially for translating solitons.

Contribution

It generalizes previous two-dimensional results to arbitrary dimensions for Lagrangian mean curvature flow with zero Maslov class.

Findings

Rigidity theorems for blow-up limits of Type II singularities.

Extension of results from 2D to higher dimensions.

Application to Lagrangian translating solitons.

Abstract

In this paper, we will prove some rigidity theorems for blow up limits to Type II singularities of Lagrangian mean curvature flow with zero Maslov class or almost calibrated Lagrangian mean curvature flows, especially for Lagrangian translating solitons in any dimension. These theorems generalized previous corresponding results from two dimensional case to arbitrarily dimensional case.