Singularities of Lagrangian mean curvature flow: monotone case

Details Singularities of Lagrangian mean curvature flow: monotone case Singularities of Lagrangian mean curvature flow: monotone case

2006-08-15

arxiv.org/abs/math/0608401v1

Mathematics

Differential Geometry

18 pages. 2 figures. Submitted

Scientific paper

We study the formation of singularities for the mean curvature flow of monotone Lagrangians in $\C^n$. 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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