Extremal domains for the first eigenvalue in a general compact Riemannian manifold

DOI10.3934/dcds.2015.35.5799zbMath1334.49131arXiv1302.4221OpenAlexW2963363839MaRDI QIDQ255569

Erwann Delay, Pieralberto Sicbaldi

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.4221

zbMATH Keywords

homogeneous spacesscalar curvaturecompact Riemannian manifoldsEinstein manifoldsLaplace-Beltrami operatorfirst eigenvalueextremal domainsgeodesic ballsperturbative methods

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Optimization of shapes other than minimal surfaces (49Q10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Local Riemannian geometry (53B20) Spectral theory; eigenvalue problems on manifolds (58C40) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25)

Related Items (8)

Piecewise smooth stationary Euler flows with compact support via overdetermined boundary problems ⋮ Nontrivial solutions to Serrin's problem in annular domains ⋮ 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 ⋮ Extremal domains of big volume for the first eigenvalue of the Laplace-Beltrami operator in a compact manifold ⋮ Extremal domains on Hadamard manifolds ⋮ Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities

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