Nondegenerate neck pinches along the mean curvature flow

Gábor Székelyhidi

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arXiv · 2603.11022

Nondegenerate neck pinches along the mean curvature flow

Gábor Székelyhidi

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Abstract

We show that for generic smooth compact initial surfaces the mean curvature flow in $\mathbb{R}^3$ has spherical or nondegenerate neck pinch singularities at the first singular time. In particular the singularities at the first singular time are isolated in spacetime. As an application we give a new approach to constructing a mean curvature flow with surgery for smooth compact initial surfaces in $\mathbb{R}^3$.

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Gábor Székelyhidi. 2026-03-11. Nondegenerate neck pinches along the mean curvature flow. https://arxiv.org/abs/2603.11022

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