Laplacian eigenvalues functionals and metric deformations on compact manifolds

Details Laplacian eigenvalues functionals and metric deformations on compact manifolds Laplacian eigenvalues functionals and metric deformations on compact manifolds

2007-01-26

arxiv.org/abs/math/0701777v1

Journal of Geometry and Physics 58, 1 (2008) 89 -- 104

Mathematics

Metric Geometry

Scientific paper

10.1016/j.geomphys.2007.09.008

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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