Total curvature and \(L ^{2}\) harmonic 1-forms on complete submanifolds in space forms
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Publication:849376
DOI10.1007/s10711-009-9392-zzbMath1187.53057OpenAlexW2035765954MaRDI QIDQ849376
Publication date: 25 February 2010
Published in: Geometriae Dedicata (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10711-009-9392-z
second fundamental formsubmanifoldmean curvaturetotal curvature\(L^2\) harmonic formsfinitely many ends
Global submanifolds (53C40) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
Related Items (21)
\(L^p\;p\)-harmonic 1-forms on submanifolds in a Hadamard 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 ⋮ On the structure of submanifolds in Euclidean space with flat normal bundle ⋮ Finiteness of non-parabolic ends on submanifolds in spheres ⋮ Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces ⋮ Mean curvature, volume and properness of isometric immersions ⋮ \(L^2\)-harmonic 1-forms on submanifolds with finite total curvature ⋮ Vanishing theorem for \(p\)-harmonic 1-forms on complete submanifolds in spheres ⋮ On the reduced \(L^2\) cohomology on complete hypersurfaces in Euclidean spaces ⋮ \(p\)-harmonic \(l\)-forms on complete noncompact submanifolds in sphere with flat normal bundle ⋮ On the structure of submanifolds in the hyperbolic space ⋮ A finiteness theorem for ends of complete manifolds supporting a Sobolev type inequality ⋮ Hypersurfaces in spheres with finite total curvature ⋮ The topological structure of conformally flat Riemannian manifolds ⋮ Vanishing theorems for \(L^2\) harmonic forms on complete submanifolds in Euclidean 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 ⋮ The non-parabolicity of infinite volume ends
Cites Work
- Harmonic functions and the structure of complete manifolds
- Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
- 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.
- On stable complete minimal hypersurfaces in R n +1
- On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold
- Sobolev and isoperimetric inequalities for riemannian submanifolds
- Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space
- A note on harmonic maps
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