Rigidity of minimal submanifolds in hyperbolic space
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Publication:2267744
DOI10.1007/s00013-009-0096-2zbMath1185.53069arXiv1002.3885OpenAlexW2002881497MaRDI QIDQ2267744
Publication date: 2 March 2010
Published in: Archiv der Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1002.3885
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)
Related Items (20)
Weighted volume growth and vanishing properties of \(f\)-minimal hypersurfaces in a weighted manifold ⋮ \(L^{p}\) harmonic 1-forms on submanifolds in spheres ⋮ Eigenvalue estimate and gap theorems for submanifolds in the hyperbolic space ⋮ \(p\)-harmonic functions and connectedness at infinity of complete submanifolds in a Riemannian manifold ⋮ \(L^{2}\) harmonic 2-forms on minimal hypersurfaces in spheres ⋮ harmonic 1-forms on hypersurfaces with finite index ⋮ Harmonic 1-forms on minimal hypersurfaces in \(\mathbb{S}^n \times \mathbb{R}\) ⋮ On the structure of complete hypersurfaces in a Riemannian manifold of nonnegative curvature and \(L^2\) harmonic forms ⋮ \(L^2\)-harmonic 1-forms on submanifolds with finite total curvature ⋮ Vanishing theorems for \(L^2\) harmonic 1-forms on complete submanifolds in a Riemannian manifold ⋮ Vanishing properties of -minimal hypersurfaces in a complete smooth metric measure space ⋮ \(L^{2p}_f\)-harmonic 1-forms on \(f\)-minimal hypersurfaces in a weighted manifold ⋮ On the structure of submanifolds in the hyperbolic space ⋮ \(L^{2}\) harmonic 1-forms on minimal submanifolds in spheres ⋮ A gap theorem on submanifolds with finite total curvature in spheres ⋮ Lindelöf’s theorem for hyperbolic catenoids ⋮ \(L^{2}\) harmonic 1-forms on minimal submanifolds in hyperbolic space ⋮ \(L^p\) harmonic 1-forms on totally real submanifolds in a complex projective space ⋮ The \(p\)-eigenvalue estimates and \(L^q\)\( p\)-harmonic forms on submanifolds of Hadamard manifolds ⋮ Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature
Cites Work
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- Complete minimal varieties in hyperbolic space
- The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
- Total scalar curvature and \(L^2\) harmonic 1-forms on a minimal hypersurface in Euclidean space
- On conformally compact Einstein manifolds.
- Gap theorems for minimal submanifolds in \(\mathbb{R}^{n+1}\)
- Minimal submanifolds with small total scalar curvature in Euclidean space
- An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
- An Estimate on the Ricci Curvature of a Submanifold and Some Applications
- Sobolev and isoperimetric inequalities for riemannian submanifolds
- Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space
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