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Laplacian eigenvalues functionals and metric deformations on compact manifolds

Ahmad El Soufi·Said Ilias
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Abstract

In this paper, we investigate critical points of the Laplacian's eigenvalues considered as functionals on the space of Riemmannian metrics or a conformal class of metrics on a compact manifold. We obtain necessary and sufficient conditions for a metric to be a critical point of such a functional. 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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BibTeXRIS

Ahmad El Soufi, Said Ilias. 2007-01-26. Laplacian eigenvalues functionals and metric deformations on compact manifolds. https://doi.org/10.1016/j.geomphys.2007.09.008

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