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

Xiaoli Han; Jiayu Li; Jun Sun

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arXiv · 2410.17850

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

Xiaoli Han·Jiayu Li·Jun Sun

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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.

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Xiaoli Han, Jiayu Li, Jun Sun. 2024-10-23. Translating Solitons to a Lagrangian mean curvature flow with zero Maslov class. https://arxiv.org/abs/2410.17850

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