Finite Time Singularities for Lagrangian Mean Curvature Flow
arXiv:1009.1083
Abstract
Given any embedded Lagrangian on a four dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class which 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.
Final version, to appear in Annals of Mathematics. Exposition improved. 46 pages