Complete minimal hypersurfaces in a hyperbolic space H⁴(-1)

2024/07/07 by Qing-Ming Cheng, Cheng, Qing-Ming, Yejuan Peng +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2407.05406

Abstract

In this paper, we study n-dimensional complete minimal hypersurfaces in a hyperbolic space Hⁿ⁺¹(-1) of constant curvature -1. We prove that a 3-dimensional complete minimal hypersurface with constant scalar curvature in H⁴(-1) satisfies S≤ (21)/(29) by making use of the Generalized Maximum Principle, where S denotes the squared norm of the second fundamental form of the hypersurface.

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