Extremal Eigenvalues of the Laplacian on Euclidean domains and closed surfaces

Abstract

We investigate properties of the sequences of extremal values that could be achieved by the eigenvalues of the Laplacian on Euclidean domains of unit volume, under Dirichlet and Neumann boundary conditions, respectively. In a second part, we study sequences of extremal eigenvalues of the Laplace-Beltrami operator on closed surfaces of unit area.

References in corpus (5)

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• On the minimization of Dirichlet eigenvalues of the Laplace operator
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Cited by in corpus (9)

• Maximising Neumann eigenvalues on rectangles
• Minimising Dirichlet eigenvalues on cuboids of unit measure
• Optimal stretching for lattice points and eigenvalues
• Families of non-tiling domains satisfying Pólya's conjecture
• Asymptotic behaviour of cuboids optimising Laplacian eigenvalues
• Shifted lattices and asymptotically optimal ellipses
• Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles
• Maximal spectral surfaces of revolution converge to a catenoid
• Geometric spectral theory of quantum graphs