Singularities of Equivariant Lagrangian Mean Curvature Flow

2019/10/14 by Wood, Albert · 1 citation
#53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.06122

Abstract

We study almost-calibrated, O(n)-equivariant Lagrangian mean curvature flow in ℂⁿ, and prove structural theorems about the Type I and Type II blowups of finite-time singularities. In particular, we prove that any Type I blowup of such a flow must be a special Lagrangian pair of transversely intersecting planes, any Type II blowup must be the Lawlor neck with the same asymptotes, and these blowups are independent of the choice of rescaling. We also give a partial classification of when singularities occur in the equivariant case, and examine the intermediate scales between the Type I and Type II models.

Cited by

• Lagrangian Translating Solitons and Special Lagrangians in ℂ^m with Symmetries

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