Unboundedness of the first eigenvalue of the Laplacian in symplectic category
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 λ1 of the Laplacian associated with it. We show that λ1 can be made arbitrarily large, when we vary the metric. This generalizes previous results of Polterovich, and of Mangoubi.
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