Singularity of Mean Curvature Flow of Lagrangian Submanifolds
Differential Geometry
2009-11-10 v1
Abstract
In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold is Lagrangian and almost calibrated by Re\Omega in a Calabi-Yau n-fold (M,\Omega), and T>0 is the first blow-up time of the mean curvature flow, then the tangent cone of the mean curvature flow at a singular point (X,T) is a stationary Lagrangian integer multiplicity current in R\sup 2n with volume density greater than one at X. When n=2, the tangent cone consists of a finite union of more than one 2-planes in R\sup 4 which are complex in a complex structure on R\sup 4.
Cite
@article{arxiv.math/0301281,
title = {Singularity of Mean Curvature Flow of Lagrangian Submanifolds},
author = {Jingyi Chen and Jiayu Li},
journal= {arXiv preprint arXiv:math/0301281},
year = {2009}
}