Finite time singularities for Lagrangian mean curvature flow

Abstract

Given any embedded Lagrangian on a four-dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class that develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lagrangian mean curvature flow.

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Authors

André Neves

Department of Mathematics
Imperial College London
South Kensington Campus
London S27 2AZ
United Kingdom