Laplacian eigenvalues functionals and metric deformations on compact manifolds
Metric Geometry
2009-11-13 v1 Differential Geometry
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.
Cite
@article{arxiv.math/0701777,
title = {Laplacian eigenvalues functionals and metric deformations on compact manifolds},
author = {Ahmad El Soufi and Said Ilias},
journal= {arXiv preprint arXiv:math/0701777},
year = {2009}
}