\(L^{2}\) harmonic 1-forms on minimal submanifolds in hyperbolic space

DOI10.1016/j.jmaa.2010.05.048zbMath1195.53087arXiv1007.0663OpenAlexW1970028261MaRDI QIDQ990836

Keomkyo Seo

Publication date: 1 September 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.0663

zbMATH Keywords

hyperbolic spacefirst eigenvalueminimal submanifolds\(L^{2}\) harmonic formssuper stable

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometric aspects of harmonic maps (53C43)

Related Items (15)

Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications ⋮ Weighted volume growth and vanishing properties of \(f\)-minimal hypersurfaces in a weighted manifold ⋮ 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 ⋮ harmonic 1-forms on hypersurfaces with finite index ⋮ 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 ⋮ \(L^p\) harmonic 1-forms on minimal hypersurfaces with finite index ⋮ Rigidity and stability estimates for minimal submanifolds in the hyperbolic space ⋮ \(L^{2p}_f\)-harmonic 1-forms on \(f\)-minimal hypersurfaces in a weighted manifold ⋮ On the structure of submanifolds in the hyperbolic space ⋮ Liouville-type theorems for weighted \(p\)-harmonic 1-forms and weighted \(p\)-harmonic maps ⋮ \(L^p\) 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

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