Local non-collapsing of volume for the Lagrangian mean curvature flow

Abstract

We prove an optimal control on the time-dependent measure of a measurable set under a reparametrized Lagrangian mean curvature flow of almost calibrated submanifolds in a Calabi-Yau manifold. Moreover we give a classification of those Lagrangian translating solitons in ${\mathbb{C}}^m$ that evolve by this reparametrized flow