Generic neck pinch singularities along 2D Lagrangian mean curvature flow

Gábor Székelyhidi

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arXiv · 2602.15771

Generic neck pinch singularities along 2D Lagrangian mean curvature flow

Gábor Székelyhidi

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Abstract

We introduce a notion of nondegenerate neck pinch singularity along the Lagrangian mean curvature flow of surfaces in a Calabi-Yau surface. We show that such singularities can occur, are stable under small perturbations, and any neck pinch singularity can be perturbed to such a nondegenerate singularity near the singular time. Using this we answer some questions raised by Neves and Joyce. We also introduce nondegenerate teardrop singularities and show that these cannot occur for embedded flows.

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Gábor Székelyhidi. 2026-02-17. Generic neck pinch singularities along 2D Lagrangian mean curvature flow. https://arxiv.org/abs/2602.15771

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