Finiteness of Index and Total Scalar Curvature for Minimal Hypersurfaces

DOI10.2307/2046961zbMath0661.53039OpenAlexW4240071674MaRDI QIDQ3810478

Johan Tysk

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2046961

zbMATH Keywords

minimal hypersurfaceindexvolume growthtotal scalar curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

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Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space, Sobolev inequality and stability of minimal submanifolds, Density and spectrum of minimal submanifolds in space forms, Minimal hypersurfaces with bounded index, CMC hypersurfaces with bounded Morse index, Index and topology of minimal hypersurfaces in \(\mathbb {R}^n\), Free boundary minimal hypersurfaces outside of the ball, harmonic 1-forms on hypersurfaces with finite index, Mean curvature, volume and properness of isometric immersions, Qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area, On the finiteness of the Morse index for Schrödinger operators, \(L^p\) harmonic 1-forms on minimal hypersurfaces with finite index, Unnamed Item, Harmonic 1-forms on immersed hypersurfaces in a Riemannian manifold with weighted bi-Ricci curvature bounded from below, Total scalar curvature and rigidity of minimal hypersurfaces in Euclidean space, Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces, Bubbling analysis and geometric convergence results for free boundary minimal surfaces, Vanishing theorems on Riemannian manifolds, and geometric applications, On the structure and volume growth of submanifolds in Riemannian manifolds, On the entropies of hypersurfaces with bounded mean curvature

Cites Work

• On the Schrödinger equation and the eigenvalue problem
• On complete minimal surfaces with finite Morse index in three manifolds
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• Eigenvalue estimates with applications to minimal surfaces
• Minimal varieties in Riemannian manifolds
• Regularity of stable minimal hypersurfaces
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ