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A stable self-shrinking Möbius bundle in ℝ4
Abstract
We prove the linear stability of an embedded mean curvature flow shrinker in ℝ4 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.
Related
- Uniqueness of self-shrinking ends asymptotic to a cylindrical cone
- A Bernstein Theorem for the Self-Shrinking J-Equation and Some Generalizations
- Shrinking Kähler-Ricci solitons on toric fano fibrations
- Complete steady and shrinking gradient Yamabe solitons
- Uniqueness of the soliton vector field of a shrinking gradient Kähler-Ricci soliton
BibTeX
@misc{braxton2026stable,
title = {{A stable self-shrinking Möbius bundle in $\mathbb R^4$}},
author = {Kahnrad Braxton and Tang-Kai Lee and Jonathan J. Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19648},
eprint = {2609.19648},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19648},
}
RIS
TY - UNPB
TI - A stable self-shrinking Möbius bundle in ℝ^4
AU - Kahnrad Braxton
AU - Tang-Kai Lee
AU - Jonathan J. Zhu
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19648
UR - https://arxiv.org/abs/2609.19648
AB - We prove the linear stability of an embedded mean curvature flow shrinker in 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.
ER -