On minimal hypersurfaces with finite harmonic indices

DOI10.1215/S0012-7094-01-11021-1zbMath1023.53046OpenAlexW2066244362WikidataQ125938986 ScholiaQ125938986MaRDI QIDQ1847873

Jia-Qiang Mei, Sen-Lin Xu

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-11021-1

zbMATH Keywords

finite total curvatureminimal hypersurfacesharmonic indexnumber of endsharmonic stability

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (2)

Index and topology of minimal hypersurfaces in \(\mathbb {R}^n\) ⋮ Complete harmonic stable minimal hypersurfaces in a Riemannian manifold

Cites Work

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• On the oriented Plateau problem
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• Positive harmonic functions on complete manifolds with non-negative curvature outside a compact set
• Stability of minimal hypersurfaces
• Schrödinger operators and index bounds for minimal submanifolds
• The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Global properties of minimal surfaces in \(E^ 3\) and \(E^ n\)
• Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• Harnack's inequality for elliptic differential equations on minimal surfaces
• Curvature estimates for minimal surfaces in $3$-manifolds
• On stable complete minimal hypersurfaces in R n +1
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Stable complete minimal surfaces in 𝑅³ are planes
• Minimal submanifolds with finite total scalar curvature
• The space of properly embedded minimal surfaces and their Fourier transforms
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ

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