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PreprintarXiv licencearXiv

Strongly stable CMC-one hypersurfaces in every hyperbolic space of dimension at least four

  • Zihao Wang
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Abstract

For every integer d≥4, we prove strong stability for a subfamily of classical rotational hypersurfaces in ℍd with normalized mean curvature one. The examples are complete, two-sided, properly embedded, and nowhere umbilic, with topology ℝ×𝕊d−2. An explicit positive supersolution yields a quantitative stability inequality for all compactly supported test functions. Consequently, endpoint horospherical rigidity fails in every ambient dimension at least four.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026strongly,
  title = {{Strongly stable CMC-one hypersurfaces in every hyperbolic space of dimension at least four}},
  author = {Zihao Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22059},
  eprint = {2609.22059},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22059},
}
RIS
TY  - UNPB
TI  - Strongly stable CMC-one hypersurfaces in every hyperbolic space of dimension at least four
AU  - Zihao Wang
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.22059
UR  - https://arxiv.org/abs/2609.22059
AB  - For every integer d≥4, we prove strong stability for a subfamily of classical rotational hypersurfaces in ℍ^d with normalized mean curvature one. The examples are complete, two-sided, properly embedded, and nowhere umbilic, with topology ℝ×𝕊^d−2. An explicit positive supersolution yields a quantitative stability inequality for all compactly supported test functions. Consequently, endpoint horospherical rigidity fails in every ambient dimension at least four.
ER  -