A pointwise approach to rigidity of almost graphical self-shrinking solutions of mean curvature flows

TL;DR

This paper establishes rigidity results for certain noncompact Lagrangian shrinkers in mean curvature flow, offering a new pointwise proof method that also simplifies existing results for graphical shrinkers.

Contribution

It introduces a novel pointwise approach to prove rigidity of noncompact Lagrangian shrinkers and simplifies proofs for graphical shrinkers in mean curvature flow.

Findings

Rigidity of noncompact Lagrangian shrinkers with single-valued Lagrangian angle.

Elementary proof for known rigidity results of graphical shrinkers.

Extension of rigidity results to almost graphical shrinkers.

Abstract

We prove rigidity of any properly immersed noncompact Lagrangian shrinker with single valued Lagrangian angle for Lagrangian mean curvature flows. Our pointwise approach also provides an ele- mentary proof to the known rigidity results for graphical and almost graphical shrinkers of mean curvature flows.