Singularity of Mean Curvature Flow of Lagrangian Submanifolds

Details Singularity of Mean Curvature Flow of Lagrangian Submanifolds Singularity of Mean Curvature Flow of Lagrangian Submanifolds

2003-01-24

arxiv.org/abs/math/0301281v1

Mathematics

Differential Geometry

Scientific paper

10.1007/s00222-003-0332-5

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.

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