Finite Time Singularities for Lagrangian Mean Curvature Flow
Differential Geometry
2012-05-09 v3 Analysis of PDEs
Symplectic Geometry
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.
Cite
@article{arxiv.1009.1083,
title = {Finite Time Singularities for Lagrangian Mean Curvature Flow},
author = {André Neves},
journal= {arXiv preprint arXiv:1009.1083},
year = {2012}
}
Comments
Final version, to appear in Annals of Mathematics. Exposition improved. 46 pages