Work

Stable Constant Mean Curvature Hypersurfaces in $\mathbb{H}^n$

Year: 2026

Type: preprint

Abstract: For every $n\geq 4$ 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 $\mathbb H^n$ 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.34283

Authors: Gaia, Filippo, Mazzeo, Rafe, Miranda, Ivan

Institutions: Stanford University, Instituto Nacional de Matemática Pura e Aplicada, IMPA Tech

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

OpenAlex ID: W7214746279

Cites: 7

Cited by:

Related to: 10