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PreprintCC BY 4.0arXiv

Isoperimetry of singular CMC hypersurfaces

  • Kobe Marshall-Stevens
  • Gongping Niu
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Abstract

We produce the first examples of singular isoperimetric boundaries with non-zero constant mean curvature in Riemannian manifolds. The main technical ingredient is establishing that, for constant mean curvature hypersurfaces containing isolated singularities modelled on strictly stable, strictly minimising regular tangent cones, weak strict stability implies local unique volume-constrained minimisation.

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Cite

BibTeXRIS
BibTeX
@misc{marshallstevens2026isoperimetry,
  title = {{Isoperimetry of singular CMC hypersurfaces}},
  author = {Kobe Marshall-Stevens and Gongping Niu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13423},
  eprint = {2610.13423},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13423},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Isoperimetry of singular CMC hypersurfaces
AU  - Kobe Marshall-Stevens
AU  - Gongping Niu
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13423
UR  - https://arxiv.org/abs/2610.13423
AB  - We produce the first examples of singular isoperimetric boundaries with non-zero constant mean curvature in Riemannian manifolds. The main technical ingredient is establishing that, for constant mean curvature hypersurfaces containing isolated singularities modelled on strictly stable, strictly minimising regular tangent cones, weak strict stability implies local unique volume-constrained minimisation.
ER  -