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arXiv · 1501.07823

On short time existence of Lagrangian mean curvature flow

Tom Begley·Kim Moore
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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.

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Tom Begley, Kim Moore. 2015-04-21. On short time existence of Lagrangian mean curvature flow. https://doi.org/10.1007/s00208-016-1420-3

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