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arXiv · 2609.19390

Mean curvature flows with cylindrical singularities II: stability and genericity

Ao Sun·Jinxin Xue
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Abstract

In [SX25], we introduced the notion of nondegenerate cylindrical singularity using the ideas from dynamical systems. In this paper, we further study the properties of these singularities, showing that they are stable under small perturbations. Furthermore, we show that we can perturb some mean curvature flow with degenerate singularities to produce nondegenerate singularities.

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Ao Sun, Jinxin Xue. 2026-09-16. Mean curvature flows with cylindrical singularities II: stability and genericity. https://arxiv.org/abs/2609.19390

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