Translating Solitons to a Lagrangian mean curvature flow with zero Maslov class

TL;DR

This paper investigates translating solitons in Lagrangian mean curvature flow with zero Maslov class, providing conditions for Type II singularities and exploring their role as potential blow-up limits, addressing open questions in the field.

Contribution

It offers a necessary condition for blow-up limits at Type II singularities and examines the possibility of Joyce-Lee-Tsui Lagrangian translating solitons as such limits.

Findings

Identifies a necessary condition for Type II singularity blow-up limits.

Analyzes the role of Joyce-Lee-Tsui translating solitons in singularity formation.

Provides insights into the structure of Lagrangian mean curvature flow with zero Maslov class.

Abstract

It is known that there is no a Type I singularity for the Lagrangian mean curvature flow with zero Maslov class. In this paper, we study translating solitons which are important models of Type II singularities. A necessary condition for a blow-up limit arising at a Type II singularity of a Lagrangian mean curvature flow with zero Maslov class is provided. As an application, we try to understand the important open question proposed by Joyce-Lee-Tsui and Neves-Tian, whether the Lagrangian translating solitons constructed by Joyce-Lee-Tsui can be a blow-up limit for a Lagrangian mean curvature flow with zero Maslov class.