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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{sun2026mean,
  title = {{Mean curvature flows with cylindrical singularities II: stability and genericity}},
  author = {Ao Sun and Jinxin Xue},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19390},
  eprint = {2609.19390},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19390},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Mean curvature flows with cylindrical singularities II: stability and genericity
AU  - Ao Sun
AU  - Jinxin Xue
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19390
UR  - https://arxiv.org/abs/2609.19390
AB  - 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.
ER  -