Rigidity and stability estimates for minimal submanifolds in the hyperbolic space

2020/06/21 by Bezerra, Adriano Cavalcante, Manfio, Fernando · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.11700

Abstract

In this paper we establish conditions on the length of the second fundamental form of a complete minimal submanifold Mⁿ in the hyperbolic space ℍ^n+m in order to show that Mⁿ is totally geodesic. We also obtain sharp upper bounds estimates for the first eigenvalue of the super stability operator in the case of M is a surface in ℍ⁴.

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