Upper bounds for the first eigenvalue of the Laplacian of hypersurfaces in terms of anisotropic mean curvatures

DOI10.1007/S00025-013-0322-XzbMath1278.53011OpenAlexW2009268307MaRDI QIDQ384012

Julien Roth

Publication date: 25 November 2013

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-013-0322-x

zbMATH Keywords

eigenvaluesLaplacianpinchinghypersurfacesanisotropic mean curvatures

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (6)

Extrinsic eigenvalues estimates for hypersurfaces in product spaces ⋮ Reilly-type inequalities for Paneitz and Steklov eigenvalues ⋮ Upper bounds for the first non-zero Steklov eigenvalue via anisotropic mean curvatures ⋮ Upper bounds for the first eigenvalue of a Jacobi type operator via anisotropic mean curvatures ⋮ Anisotropic eigenvalues upper bounds for hypersurfaces in weighted Euclidean spaces ⋮ Pinching of the first eigenvalue for second order operators on hypersurfaces of the Euclidean space

Cites Work

• Unnamed Item
• Unnamed Item
• Eigenvalue pinching and application to the stability and the almost umbilicity of hypersurfaces
• Some characterizations of the Wulff shape
• A characteristic property of spheres
• A pinching theorem for the first eigenvalue of the Laplacian on hypersurfaces of the Euclidean space
• A new variational characterization of the Wulff shape
• Integral formula of Minkowski type and new characterization of the Wulff shape
• On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space
• Pinching of the first eigenvalue of the Laplacian and almost-Einstein hypersurfaces of the Euclidean space
• Minimal immersions of Riemannian manifolds
• Geometry and stability of surfaces with constant anisotropic mean curvature
• Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• A correction to: Sobolev and isoperimetric inequalities for riemannian submanifolds
• Stability of the Wulff shape
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
• Some integral formulas for closed hypersurfaces

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