Mean Curvature Flows of Two-Convex Lagrangians

Abstract

We prove regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case. Such results were previously only known in the convex case, of which the current work represents a significant improvement. The proof relies on a newly discovered monotone quantity that controls two-convexity. Through a unitary transformation, same result for the mean curvature flow of area-decreasing Lagrangian submanifolds were established.