On short time existence of Lagrangian mean curvature flow

2016/05/07 by Tom Begley, Kim Moore
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.1007/s00208-016-1420-3

Abstract

We consider a short time existence problem motivated by a conjecture of Joyce (Conjectures on Bridgeland stability for Fukaya categories of Calabi–Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow. arXiv:1401.4949 , 2014). Specifically we prove that given any compact Lagrangian L⊂ \mathbb Cⁿ with a finite number of singularities, each asymptotic to a pair of non-area-minimising, transversally intersecting Lagrangian planes, there is a smooth Lagrangian mean curvature flow existing for some positive time, that attains L as t \searrow 0 as varifolds, and smoothly locally away from the singularities.

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