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PreprintCC BY 4.0arXiv

Stable Constant Mean Curvature Hypersurfaces in ℍn

  • Filippo Gaia
  • Rafe Mazzeo
  • Ivan Miranda
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Abstract

For every n≥ 4 and every H in a neighborhood of n−1 (depending on n), we prove the existence of a properly embedded strongly stable CMC hypersurface in ℍn with mean curvature H and infinitely many ends, invariant under the action of a Schottky group. In particular, stable Bernstein-type rigidity fails in this range.

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Cite

BibTeXRIS
BibTeX
@misc{gaia2026stable,
  title = {{Stable Constant Mean Curvature Hypersurfaces in $\mathbbH^n$}},
  author = {Filippo Gaia and Rafe Mazzeo and Ivan Miranda},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34283},
  eprint = {2609.34283},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34283},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stable Constant Mean Curvature Hypersurfaces in ℍ^n
AU  - Filippo Gaia
AU  - Rafe Mazzeo
AU  - Ivan Miranda
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34283
UR  - https://arxiv.org/abs/2609.34283
AB  - For every n≥ 4 and every H in a neighborhood of n−1 (depending on n), we prove the existence of a properly embedded strongly stable CMC hypersurface in ℍ^n with mean curvature H and infinitely many ends, invariant under the action of a Schottky group. In particular, stable Bernstein-type rigidity fails in this range.
ER  -