Variational aspects of Laplace eigenvalues on Riemannian surfaces

Gerasim Kokarev

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arXiv · 1103.2448

Variational aspects of Laplace eigenvalues on Riemannian surfaces

Gerasim Kokarev

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Abstract

We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the general regularity properties of $λ_k$-extremal metrics and the existence of a partially regular $λ_1$-maximiser.

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BibTeX RIS

Gerasim Kokarev. 2014-03-12. Variational aspects of Laplace eigenvalues on Riemannian surfaces. https://arxiv.org/abs/1103.2448

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