A spectral characterization of the $H(r)$-torus by the first stability eigenvalue

DOI10.1090/S0002-9939-04-07559-8zbMath1065.53046OpenAlexW1484764207MaRDI QIDQ4829911

Luis J. Alías, Abdênago A. Barros, Aldir Brasil Junior

Publication date: 1 December 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-04-07559-8

zbMATH Keywords

constant mean curvaturefirst eigenvalue

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (20)

On the first stability eigenvalue of closed submanifolds in the Euclidean and hyperbolic spaces ⋮ A new optimal estimate for the first stability eigenvalue of closed hypersurfaces in Riemannian space forms ⋮ First stability eigenvalue of singular hypersurfaces with constant mean curvature in the unit sphere ⋮ Upper bounds for the first stability eigenvalue of surfaces in 3-Riemannian manifolds ⋮ A half-space type property in the Euclidean sphere ⋮ On the first strong stability eigenvalue of closed submanifolds in the unit sphere ⋮ Eigenvalue estimates for the stability operator of CMC compact surfaces in three-dimensional warped products ⋮ Sharp estimates for the first stability eigenvalue of surfaces in the presence of a closed conformal vector field ⋮ First eigenvalue of a Jacobi operator of hypersurfaces with a constant scalar curvature ⋮ New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms ⋮ First stability eigenvalue characterization of CMC Hopf tori into Riemannian Killing submersions ⋮ Estimates for the first eigenvalue of Jacobi operator on hypersurfaces with constant mean curvature in spheres ⋮ Unnamed Item ⋮ On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds ⋮ On the first stability eigenvalue of CMC surfaces into warped products with two-dimensional fiber ⋮ Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces ⋮ A lower bound for 𝐿₂ length of second fundamental form on minimal hypersurfaces ⋮ On the first stability eigenvalue of hypersurfaces in the Euclidean and hyperbolic spaces ⋮ First \(\frac{2}{n}\)-stability eigenvalue of singular minimal hypersurfaces in space forms ⋮ An estimate of the first eigenvalue of a Schrödinger operator on closed surfaces

Cites Work

• New characterizations of the Clifford tori and the Veronese surface
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• Upper bound for the second eigenvalue of a Schrödinger operator on a compact manifold and applications
• Second eigenvalue of Schrödinger operators and mean curvature
• Eigenvalue and ``twisted eigenvalue problems, applications to CMC surfaces
• A new characterization of submanifolds with parallel mean curvature vector in \(S^{n+p}\)
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• Hypersurfaces and a Pinching Problem on the Second Fundamental Tensor
• Hypersurfaces with Constant Mean Curvature in Spheres
• First stability eigenvalue characterization of Clifford hypersurfaces
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

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