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On short time existence of Lagrangian mean curvature flow


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Authors

Begley, Tom 
Moore, Kim 

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⊂CnL⊂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↘0t↘0 as varifolds, and smoothly locally away from the singularities.

Description

This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Springer.

Keywords

4901 Applied Mathematics, 4902 Mathematical Physics, 4903 Numerical and Computational Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

Mathematische Annalen

Conference Name

Journal ISSN

0025-5831
1432-1807

Volume Title

Publisher

Springer Nature
Sponsorship
Both authors supported by EPSRC grant EP/H023348/1 at the Cambridge Centre for Analysis.