Extremal domains for the first eigenvalue of the Laplace-Beltrami operator

DOI10.5802/aif.2438zbMath1166.53029OpenAlexW2237975890MaRDI QIDQ1013019

Pieralberto Sicbaldi, Frank Pacard

Publication date: 29 April 2009

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2009__59_2_515_0

zbMATH Keywords

scalar curvatureLaplace-Beltrami operatorfirst eigenvaluegeodesic sphereextremal domain

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

New extremal domains for the first eigenvalue of the Laplacian in flat tori, Heat flow, heat content and the isoparametric property, Piecewise smooth stationary Euler flows with compact support via overdetermined boundary problems, Sharp local estimates for the Szegő-Weinberger profile in Riemannian manifolds, Existence and regularity of Faber-Krahn minimizers in a Riemannian manifold, Overdetermined elliptic problems in nontrivial contractible domains of the sphere, Overdetermined boundary problems with nonconstant Dirichlet and Neumann data, A Riemannian Point of View for a Quadrature Surface Free Boundary Problem, A short survey on overdetermined elliptic problems in unbounded domains, Maximization of Laplace−Beltrami eigenvalues on closed Riemannian surfaces, Bifurcating extremal domains for the first eigenvalue of the Laplacian, Extremal domains of big volume for the first eigenvalue of the Laplace-Beltrami operator in a compact manifold, Asymptotic expansion of the Faber-Krahn profile of a compact Riemannian manifold, Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities, Isoperimetry for semilinear torsion problems in Riemannian two-manifolds, Overdetermined Problems for Some Fully Non Linear Operators, Some local eigenvalue estimates involving curvatures, Extremal domains for the first eigenvalue in a general compact Riemannian manifold

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Foliation by constant mean curvature spheres
• Constant mean curvature spheres in Riemannian manifolds
• Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold
• The Yamabe problem
• Sharp local isoperimetric inequalities involving the scalar curvature
• Eigenvalue variations for the Neumann problem