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 (2)

• Extremal eigenvalues of the Laplacian in a conformal class of metrics : the "conformal spectrum"
• How large can the first eigenvalue be on a surface of genus two?

Cited by in corpus (9)

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• Optimal stretching for lattice points and eigenvalues
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• 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