English

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

Differential Geometry 2025-02-17 v2

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.

Keywords

Cite

@article{arxiv.2410.17850,
  title  = {Translating Solitons to a Lagrangian mean curvature flow with zero Maslov class},
  author = {Xiaoli Han and Jiayu Li and Jun Sun},
  journal= {arXiv preprint arXiv:2410.17850},
  year   = {2025}
}

Comments

There are some gaps in the proof of the main theorems in the previous version. We add some natural assumptions for the main result in the present version