Abstract
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 (X 0,T) is a stationary Lagrangian integer multiplicity current in R 2n with volume density greater than one at X 0. When n=2, the tangent cone is a finite union of at least two 2-planes in R 4 which are complex in a complex structure on R 4.
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Chen, J., Li, J. Singularity of mean curvature flow of Lagrangian submanifolds. Invent. math. 156, 25–51 (2004). https://doi.org/10.1007/s00222-003-0332-5
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DOI: https://doi.org/10.1007/s00222-003-0332-5