Upper bounds for the first non-zero Steklov eigenvalue via anisotropic mean curvatures

DOI10.1007/s00025-021-01544-wzbMath1491.53047OpenAlexW3213894669MaRDI QIDQ2242609

Yanyan Li

Publication date: 10 November 2021

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

Full work available at URL: https://doi.org/10.1007/s00025-021-01544-w

zbMATH Keywords

eigenvaluesoperator in divergence formSteklov problempinching resultsHsiung-Minkowski type formulas

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 (1)

Some recent developments on the Steklov eigenvalue problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Upper bounds for the first eigenvalue of the Laplacian of hypersurfaces in terms of anisotropic mean curvatures
• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• Some characterizations of the Wulff shape
• A Reilly inequality for the first Steklov eigenvalue
• A pinching theorem for the first eigenvalue of the Laplacian on hypersurfaces of the Euclidean space
• Integral formula of Minkowski type and new characterization of the Wulff shape
• Some inequalities for Stekloff eigenvalues
• The relative differential geometry of nonparametric hypersurfaces
• An inequality for Steklov eigenvalues for planar domains
• The geometry of the first non-zero Stekloff eigenvalue
• A finite element solution of an added mass formulation for coupled fluid-solid vibrations
• Inequalities for the Steklov eigenvalues
• A Reilly inequality for the first non-zero eigenvalue of a class of operators on Riemannian manifold
• 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
• Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• Elliptic Equations in Divergence Form, Geometric Critical Points of Solutions, and Stekloff Eigenfunctions

This page was built for publication: Upper bounds for the first non-zero Steklov eigenvalue via anisotropic mean curvatures