On short time existence of Lagrangian mean curvature flow

Abstract

We consider a short time existence problem motivated by a conjecture of Joyce. Specifically we prove that given any compact Lagrangian $L\subset {\mathbb{C}}^n$ 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.

37 pages. Updated references for high-codimension interior estimates

References in corpus (3)

• Singularities of Lagrangian mean curvature flow: zero-Maslov class case
• Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in C^m
• Recent Progress on Singularities of Lagrangian Mean Curvature Flow

Cited by in corpus (3)

• Uniqueness of asymptotically conical tangent flows
• Approximation of mean curvature flow with generic singularities by smooth flows with surgery
• On $n$-dimensional complete self-similar solutions to the mean curvature flow in ${\mathbb{R}}^{n+1}$ with nonnegative constant scalar curvature