Title: Rigidity and stability estimates for minimal submanifolds in the hyperbolic space
Abstract: In this paper we establish conditions on the length of the second fundamental form of a complete minimal submanifold $M^n$ in the hyperbolic space $\mathbb{H}^{n+m}$ in order to show that $M^n$ 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 $\mathbb{H}^{4}$.
Publication Year: 2020
Publication Date: 2020-06-21
Language: en
Type: preprint
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot