\(L^2\)-harmonic 1-forms on submanifolds with finite total curvature

DOI10.1007/s12220-012-9334-0zbMath1308.53056arXiv1201.5392OpenAlexW2110288551WikidataQ126193150 ScholiaQ126193150MaRDI QIDQ471998

Heudson Mirandola, Marcos Petrúcio De A. Cavalcante, Feliciano Vitorio

Publication date: 18 November 2014

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.5392

zbMATH Keywords

finite total curvatureisometric immersion\(L^2\)-harmonic 1-formtraceless second fundamental form

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (31)

Geometries and topologies of conformally flat Riemannian manifolds ⋮ Harmonic \(p\)-forms on Hadamard manifolds with finite total curvature ⋮ \(L^p\;p\)-harmonic 1-forms on submanifolds in a Hadamard manifold ⋮ Weighted volume growth and vanishing properties of \(f\)-minimal hypersurfaces in a weighted manifold ⋮ VANISHING THEOREMS FOR HYPERSURFACES IN THE UNIT SPHERE ⋮ \(L^{p}\) harmonic 1-forms on submanifolds in spheres ⋮ Eigenvalue estimate and gap theorems for submanifolds in the hyperbolic space ⋮ The topological structure of complete noncompact submanifolds in spheres ⋮ \(p\)-harmonic functions and connectedness at infinity of complete submanifolds in a Riemannian manifold ⋮ On the structure of submanifolds in Euclidean space with flat normal bundle ⋮ Finiteness of non-parabolic ends on submanifolds in spheres ⋮ harmonic 1-forms on hypersurfaces with finite index ⋮ Unnamed Item ⋮ Vanishing theorems for \(L^2\) harmonic 1-forms on complete submanifolds in a Riemannian manifold ⋮ Vanishing theorem for \(p\)-harmonic 1-forms on complete submanifolds in spheres ⋮ On the reduced \(L^2\) cohomology on complete hypersurfaces in Euclidean spaces ⋮ Vanishing properties of -minimal hypersurfaces in a complete smooth metric measure space ⋮ \(p\)-harmonic \(l\)-forms on complete noncompact submanifolds in sphere with flat normal bundle ⋮ \(L^p\) harmonic 1-forms on minimal hypersurfaces with finite index ⋮ On the structure of submanifolds in the hyperbolic space ⋮ Hypersurfaces in spheres with finite total curvature ⋮ Unnamed Item ⋮ The topological structure of conformally flat Riemannian manifolds ⋮ Vanishing theorems for \(p\)-harmonic \(\ell\)-forms on Riemannian manifolds with a weighted Poincaré inequality ⋮ Vanishing theorems for \(L^2\) harmonic forms on complete submanifolds in Euclidean space ⋮ Harmonic 1-forms on immersed hypersurfaces in a Riemannian manifold with weighted bi-Ricci curvature bounded from below ⋮ On reduced L2 cohomology of hypersurfaces in spheres with finite total curvature ⋮ \(L^p\) 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 ⋮ \(L^p\) harmonic 1-forms on conformally flat Riemannian manifolds ⋮ Gap theorems on hypersurfaces in spheres

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