On the second boundary value problem for Lagrangian mean curvature flow

TL;DR

This paper studies a nonlinear parabolic equation with boundary conditions, proving long-term existence and convergence, and applies these results to minimal Lagrangian graphs boundary value problems.

Contribution

It establishes the long-time existence and convergence of the Lagrangian mean curvature flow with nonlinear boundary conditions, and applies these findings to minimal Lagrangian graph boundary problems.

Findings

Proved long-time existence of the flow.

Established convergence of the flow.

Applied results to minimal Lagrangian graphs.

Abstract

We consider a fully nonlinear parabolic equation with nonlinear Neumann type boundary condition, and show that the longtime existence and convergence of the flow. Finally we apply this study to the boundary value problem for minimal Lagrangian graphs.