Rigidity theorems for minimal submanifolds in a hyperbolic space

摘要

Let M be a complete immersed minimal hypersurface in a hyperbolic space. In this paper we establish conditions on the first eigenvalue of the stability and super stability operators and the Ld norm of the length of the second fundamental form of M to imply that M is totally geodesic. Similar results for minimal submanifolds in a hyperbolic space are also proven.