Unboundedness of the first eigenvalue of the Laplacian in symplectic category
arXiv:1207.3829 · doi:10.1142/S1793525313500040
Abstract
Given a closed symplectic manifold (M,ω) of dimension greater than 2, we consider all Riemannian metrics on M, which are compatible with the symplectic structure ω. For each such metric, we look at the first eigenvalue λ_1 of the Laplacian associated with it. We show that λ_1 can be made arbitrarily large, when we vary the metric. This generalizes previous results of Polterovich, and of Mangoubi.
arXiv commentThe paper has been withdrawn by the author due to copyright issues. The paper appeared in print, Journal of Topology and Analysis, Vol. 5, No. 1 (2013) pp 13-56