A Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase

TL;DR

This paper establishes interior a priori estimates for singularities in the Lagrangian mean curvature flow under supercritical phase conditions, extending to broader classes of related equations.

Contribution

It introduces a Jacobi inequality applicable to critical and supercritical phases, advancing understanding of singularity behavior in Lagrangian mean curvature flow.

Findings

Proved interior a priori estimates for singularities.

Extended results to broader Lagrangian mean curvature equations.

Established a Jacobi inequality for supercritical phases.

Abstract

In this paper, we prove interior a priori estimates for singularities of the Lagrangian mean curvature flow assuming the Lagrangian phase is supercritical. We prove a Jacobi inequality that holds good when the Lagrangian phase is critical and supercritical. We further extend our results to a broader class of Lagrangian mean curvature type equations.