Variational aspects of Laplace eigenvalues on Riemannian surfaces

Gerasim Kokarev

Variational aspects of Laplace eigenvalues on Riemannian surfaces

Spectral Theory 2014-03-13 v3 Differential Geometry

Authors: Gerasim Kokarev

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 $\lambda_k$ -extremal metrics and the existence of a partially regular $\lambda_1$ -maximiser.

Keywords

Laplace eigenvalues Riemannian surfaces conformal metrics calculus of variations extremal metrics regularity

Cite

@article{arxiv.1103.2448,
  title  = {Variational aspects of Laplace eigenvalues on Riemannian surfaces},
  author = {Gerasim Kokarev},
  journal= {arXiv preprint arXiv:1103.2448},
  year   = {2014}
}

Comments

revised version, 38 pages; re-written introduction, changes taking into account referee comments made, misprints corrected, new references added, to appear in Advances in Mathematics

Variational aspects of Laplace eigenvalues on Riemannian surfaces

Abstract

Keywords

Cite

Comments

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