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arXiv · 2410.22172

Singularity formations in Lagrangian mean curvature flow

Yang Li·Gábor Székelyhidi
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Abstract

We study singularities along the Lagrangian mean curvature flow with tangent flows given by multiplicity one special Lagrangian cones that are smooth away from the origin. Some results are: uniqueness of all such tangent flows in dimension two; uniqueness in any dimension when the link of the cone is connected; the existence of nontrivial special Lagrangian blowup limits. We also prove a singular version of Imagi-Joyce-dos Santos's uniqueness result of the Lawlor neck. As an application we prove that in any dimension, singularities that admit a tangent flow given by the union of two transverse planes is modeled on shrinking Lawlor necks at suitable scales.

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Yang Li, Gábor Székelyhidi. 2024-10-29. Singularity formations in Lagrangian mean curvature flow. https://arxiv.org/abs/2410.22172

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