Extremal eigenvalues of the Laplacian on Euclidean domains and closed surfaces

DOI10.1007/s00209-014-1325-3zbMath1301.35063arXiv1403.1993OpenAlexW2009988323MaRDI QIDQ463989

Bruno Colbois, Ahmad El Soufi

Publication date: 17 October 2014

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.1993

zbMATH Keywords

Laplace-Beltrami operatorextremal eigenvaluesLaplacianspectral geometryclosed surfaces

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Critical metrics (58E11) PDEs on manifolds (35R01)

Related Items (12)

Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction ⋮ Shifted lattices and asymptotically optimal ellipses ⋮ Bounds and extremal domains for Robin eigenvalues with negative boundary parameter ⋮ Asymptotic behaviour of extremal averages of Laplacian eigenvalues ⋮ Asymptotic behaviour of cuboids optimising Laplacian eigenvalues ⋮ Families of non-tiling domains satisfying Pólya’s conjecture ⋮ MINIMIZING DIRICHLET EIGENVALUES ON CUBOIDS OF UNIT MEASURE ⋮ Maximization of Laplace−Beltrami eigenvalues on closed Riemannian surfaces ⋮ Some results on higher eigenvalue optimization ⋮ Numerical optimization of low eigenvalues of the Dirichlet and Neumann laplacians ⋮ Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles ⋮ Maximising Neumann eigenvalues on rectangles

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