Singularities of Lagrangian mean curvature flow: monotone case

2006/08/15 by Neves, Andre'
#53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.math/0608401

Abstract

We study the formation of singularities for the mean curvature flow of monotone Lagrangians in \Cⁿ. More precisely, we show that if singularities happen before a critical time then the tangent flow can be decomposed into a finite union of area-minimizing Lagrangian cones (Slag cones). When n=2, we can improve this result by showing that connected components of the rescaled flow converge to an area-minimizing cone, as opposed to possible non-area minimizing union of Slag cones. In the last section, we give specific examples for which such singularity formation occurs.

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