Rigidity of minimal submanifolds in hyperbolic space

Abstract

We prove that if an $n$-dimensional complete minimal submanifold $M$ in hyperbolic space has sufficiently small total scalar curvature then $M$ has only one end. We also prove that for such $M$ there exist no nontrivial $L^2$ harmonic 1-forms on $M$.

Cited by in corpus (2)

• $L^2$ harmonic 1-forms on minimal submanifolds in hyperbolic space
• Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature