Singularity of Mean Curvature Flow of Lagrangian Submanifolds
نویسندگان
چکیده
In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold Σ0 is Lagrangian and almost calibrated by ReΩ in a Calabi-Yau n-fold (M,Ω), 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 (X0, T ) is a stationary Lagrangian integer multiplicity current in R2n with volume density greater than one at X0. When n = 2, the tangent cone consists of a finite union of more than one 2-planes in R4 which are complex in a complex structure on R4.
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