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arXiv · 1207.3829

Unboundedness of the first eigenvalue of the Laplacian in symplectic category

Lev Buhovsky
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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.

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Lev Buhovsky. 2013-08-22. Unboundedness of the first eigenvalue of the Laplacian in symplectic category. https://doi.org/10.1142/s1793525313500040

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