The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow

TL;DR

This paper establishes rigidity results for the Clifford torus, demonstrating its unique properties as a compact self-shrinker in Lagrangian mean curvature flow, contributing to understanding its geometric stability.

Contribution

It presents new rigidity theorems characterizing the Clifford torus among compact self-shrinkers in Lagrangian mean curvature flow.

Findings

Rigidity results for the Clifford torus as a self-shrinker

Characterization of the Clifford torus's uniqueness in the flow

Insights into the geometric stability of the Clifford torus

Abstract

We provide several rigidity results for the Clifford torus in the class of compact self-shrinkers for Lagrangian mean curvature flow.