On Short Time Existence of Lagrangian Mean Curvature Flow

Abstract

We consider a short time existence problem motivated by a conjecture of Joyce in [8]. Specifically we prove that given any compact Lagrangian L ⊂ C^n with a finite number of singularities, each asymptotic to a pair of nonarea-minimising, transversally intersecting Lagrangian planes, there is a smooth Lagrangian mean curvature flow existing for some positive time, that attains L as t ↘ 0 as varifolds, and smoothly locally away from the singularities.