English

Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$

Differential Geometry 2025-08-27 v1

Abstract

In this paper, we study nn-dimensional complete minimal hypersurfaces in a hyperbolic space Hn+1(1)H^{n+1}(-1) of constant curvature 1-1. We prove that a 33-dimensional complete minimal hypersurface with constant scalar curvature in H4(1)H^{4}(-1) satisfies S2129S\leq \frac{21}{29} by making use of the Generalized Maximum Principle, where SS denotes the squared norm of the second fundamental form of the hypersurface.

Keywords

Cite

@article{arxiv.2407.05406,
  title  = {Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$},
  author = {Qing-Ming Cheng and Yejuan Peng},
  journal= {arXiv preprint arXiv:2407.05406},
  year   = {2025}
}

Comments

17pages

R2 v1 2026-06-28T17:31:57.234Z