Structure of stable minimal hypersurfaces in a Riemannian manifold of nonnegative Ricci curvature (Q2843792)
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scientific article; zbMATH DE number 6201382
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Structure of stable minimal hypersurfaces in a Riemannian manifold of nonnegative Ricci curvature |
scientific article; zbMATH DE number 6201382 |
Statements
26 August 2013
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stable minimal hypersurface
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Riemannian manifold
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Ricci curvature
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Bernstein problem
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parabolicity
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end
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Structure of stable minimal hypersurfaces in a Riemannian manifold of nonnegative Ricci curvature (English)
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Assume that \(N\) is a complete Riemannian manifold with nonnegative Ricci curvature and let \(M\) be a complete noncompact oriented stable minimal hypersurface in \(N\). The authors prove that if \(M\) has at least two ends and NEWLINE\[NEWLINE\int_M|A|^2\,dv= \infty,NEWLINE\]NEWLINE then \(M\) admits a nonconstant harmonic function with finite Dirichlet integral, where \(A\) is the second fundamental form of \(M\).
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