A Reilly inequality for the first non-zero eigenvalue of a class of operators on Riemannian manifold

DOI10.1007/s00574-017-0066-4zbMath1401.53027OpenAlexW2771757995WikidataQ115385734 ScholiaQ115385734MaRDI QIDQ1992232

Yanyan Li

Publication date: 2 November 2018

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-017-0066-4

zbMATH Keywords

eigenvaluesHsiung-Minkowski formulasoperator in divergence formRayleigh-Ritz inequality

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (2)

Some recent developments on the Steklov eigenvalue problem ⋮ Upper bounds for the first non-zero Steklov eigenvalue via anisotropic mean curvatures

Cites Work

• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds
• A Reilly inequality for the first Steklov eigenvalue
• Some inequalities for Stekloff eigenvalues
• On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space
• An inequality for Steklov eigenvalues for planar domains
• Extrinsic upper bound for the first eigenvalue of elliptic operators
• Upper bounds for the first eigenvalue of the Laplacian on compact submanifolds.
• Extreme principles and isoperimetric inequalities for some mixed problems of Stekloff's type
• New isoperimetric inequalities for eigenvalues and other physical quantities
• Some isoperimetric inequalities with application to the Stekloff problem
• Some integral formulas for closed hypersurfaces
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