Finite time singularities for Lagrangian mean curvature flow


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.


André Neves

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