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PreprintCC BY 4.0arXiv

Morse resolution of mean curvature flows with cylindrical singularities

  • Richard H. Bamler
  • Felix Schulze
  • Lu Wang
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Abstract

We show that a compact mean curvature flow whose singularities have multiplicity-one cylindrical tangent flows admits a smooth Morse resolution. The resolution agrees with the spacetime track outside any prescribed neighborhood of its singular set and all its critical points have the expected index. No nondegeneracy or isolatedness assumption is required. In the mean-convex case the result follows by smoothing the global arrival function.

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Cite

BibTeXRIS
BibTeX
@misc{bamler2026morse,
  title = {{Morse resolution of mean curvature flows with cylindrical singularities}},
  author = {Richard H. Bamler and Felix Schulze and Lu Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18687},
  eprint = {2609.18687},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18687},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Morse resolution of mean curvature flows with cylindrical singularities
AU  - Richard H. Bamler
AU  - Felix Schulze
AU  - Lu Wang
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18687
UR  - https://arxiv.org/abs/2609.18687
AB  - We show that a compact mean curvature flow whose singularities have multiplicity-one cylindrical tangent flows admits a smooth Morse resolution. The resolution agrees with the spacetime track outside any prescribed neighborhood of its singular set and all its critical points have the expected index. No nondegeneracy or isolatedness assumption is required. In the mean-convex case the result follows by smoothing the global arrival function.
ER  -