Lagrangian mean curvature flow in Pseudo-Euclidean space

TL;DR

This paper proves that entire Lagrangian graphs in Pseudo-Euclidean space evolve smoothly and converge under mean curvature flow, linking it to logarithmic gradient flow.

Contribution

It establishes long-term existence and convergence results for Lagrangian mean curvature flow in Pseudo-Euclidean space, a novel extension in geometric analysis.

Findings

Proves longtime existence of the flow.

Shows convergence of the flow.

Connects mean curvature flow to logarithmic gradient flow.

Abstract

We establish the longtime existence and convergence results of the mean curvature flow of entire Lagrangian graphs in Pseudo-Euclidean space which is related to Logarithmic gradient flow.