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

Fuente: arXiv
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Main Authors: Cheng, Qing-Ming, Peng, Yejuan
Format: Preprint
Published: 2024
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author Cheng, Qing-Ming
Peng, Yejuan
author_facet Cheng, Qing-Ming
Peng, Yejuan
contents In this paper, we study $n$-dimensional complete minimal hypersurfaces in a hyperbolic space $H^{n+1}(-1)$ of constant curvature $-1$. We prove that a $3$-dimensional complete minimal hypersurface with constant scalar curvature in $H^{4}(-1)$ satisfies $S\leq \frac{21}{29}$ by making use of the Generalized Maximum Principle, where $S$ denotes the squared norm of the second fundamental form of the hypersurface.
format Preprint
id arxiv_https___arxiv_org_abs_2407_05406
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$
Cheng, Qing-Ming
Peng, Yejuan
Differential Geometry
In this paper, we study $n$-dimensional complete minimal hypersurfaces in a hyperbolic space $H^{n+1}(-1)$ of constant curvature $-1$. We prove that a $3$-dimensional complete minimal hypersurface with constant scalar curvature in $H^{4}(-1)$ satisfies $S\leq \frac{21}{29}$ by making use of the Generalized Maximum Principle, where $S$ denotes the squared norm of the second fundamental form of the hypersurface.
title Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$
topic Differential Geometry
url https://arxiv.org/abs/2407.05406