Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature

TL;DR

This paper proves that there are no eternal solutions to almost-calibrated Lagrangian mean curvature flow in complex Euclidean space, using a mean curvature estimate to establish non-existence.

Contribution

It introduces a mean curvature estimate that leads to the first non-existence result for eternal solutions in this geometric flow setting.

Findings

No eternal solutions exist for almost-calibrated Lagrangian mean curvature flow.

The mean curvature estimate is a key tool for the non-existence proof.

Results apply to translating solutions as well.

Abstract

In this paper, we derive a mean curvature estimate for eternal solutions (including translating solutions) of almost-calibrated Lagrangian mean curvature flow in complex Euclidean space. As a consequence, we show a non-existence result for eternal solutions of almost-calibrated Lagrangian mean curvature flow.