Lagrangian Mean Curvature flow for entire Lipschitz graphs II

Abstract

We prove longtime existence and estimates for solutions to a fully nonlinear Lagrangian parabolic equation with locally $C^{1,1}$ initial data $u_0$ satisfying either (1) $-(1+\eta )I_n\le D^2{u}_0\le (1+\eta )I_n$ for some positive dimensional constant $\eta$, (2) $u_0$ is weakly convex everywhere or (3) $u_0$ satisfies a large supercritical Lagrangian phase condition.

17 pages

References in corpus (1)

• Uniqueness of viscosity solutions of a geometric fully nonlinear parabolic equation

Cited by in corpus (2)

• Entire self-similar solutions to Lagrangian Mean curvature flow
• Rigidity of Entire self-shrinking solutions to curvature flows