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 $M$.

References in corpus (1)

• The structure of stable minimal hypersurfaces in R^n

Cited by in corpus (5)

• $L^2$-harmonic $p$-forms on submanifolds with finite total curvature
• $L^2$ harmonic 1-forms on minimal submanifolds in hyperbolic space
• Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature
• Real analytic complete non-compact surfaces in Euclidean space with finite total curvature arising as solutions to ODEs
• L^2 Harmonic 1-forms on submanifolds with finite total curvature