A Liouville type theorem for ancient Lagrangian mean curvature flows

TL;DR

This paper establishes a Liouville type theorem for convex solutions of the Lagrangian mean curvature flow, demonstrating that under certain growth conditions, solutions must be trivial.

Contribution

It provides a new Liouville theorem for ancient solutions of Lagrangian mean curvature flow with specific growth restrictions.

Findings

Convex ancient solutions with quadratic growth are trivial.

The theorem applies under restricted growth assumptions.

Results contribute to understanding the rigidity of solutions.

Abstract

We prove a Liouville type result for convex solutions of the Lagrangian mean curvature flow with restricted quadratic growth assumptions at antiquity on the solutions.