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arXiv · 2609.19648

A stable self-shrinking Möbius bundle in $\mathbb R^4$

Kahnrad Braxton·Tang-Kai Lee·Jonathan J. Zhu
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Abstract

We prove the linear stability of an embedded mean curvature flow shrinker in $\mathbb R^4$ with the topology of the Möbius bundle. This provides a non-flat, non-spherical stable shrinker in higher codimension, in sharp contrast with the classification of stable hypersurface shrinkers. Topologically, the Möbius shrinker models the reversal of a real blow-up, suggesting that stable higher-codimension singularities may encode non-trivial topological operations under mean curvature flow.

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Kahnrad Braxton, Tang-Kai Lee, Jonathan J. Zhu. 2026-09-17. A stable self-shrinking Möbius bundle in $\mathbb R^4$. https://arxiv.org/abs/2609.19648

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