Laplacian eigenvalue functionals and metric deformations on compact manifolds |
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Authors: | Ahmad El Soufi,Saï d Ilias |
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Affiliation: | Université de Tours, Laboratoire de Mathématiques et Physique Théorique, UMR-CNRS 6083, Parc de Grandmont, 37200 Tours, France |
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Abstract: | In this paper, we investigate critical points of the eigenvalues of the Laplace operator considered as functionals on the space of Riemannian metrics or a conformal class of metrics on a compact manifold. We introduce a natural notion of the critical metric of such a functional and obtain necessary and sufficient conditions for a metric to be critical. We derive specific consequences concerning possible locally maximizing metrics. We also characterize critical metrics of the ratio of two consecutive eigenvalues. |
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Keywords: | 49R50 35P99 58J50 |
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