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. © 2013 Department of Mathematics, Princeton University.