Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898898 | Journal of Geometry and Physics | 2008 | 16 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Ahmad El Soufi, Saïd Ilias,