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Spectral Flexibility of the Symplectic Manifold T^2 x M | | Dan Mangoubi
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7 Aug 2005 | | Subject: | Spectral Theory; Symplectic Geometry MSC-class: 35P15; 53D05; 53C17 | math.SP math.SG | | Abstract: | We consider Riemannian metrics compatible with the symplectic structure on T^2 x M, where T^2 is a symplectic 2-Torus and M is a closed symplectic manifold. To each such metric we attach the corresponding Laplacian and consider its first positive eigenvalue lambda_1. We show that lambda_1 can be made arbitrarily large by deforming the metric structure, keeping the symplectic structure fixed. This extends a theorem of L. Polterovich on T^4 x M. The conjecture is that the same is true for any symplectic manifold of dimension >= 4. | | Source: | arXiv, math.SP/0508128 | | Services: | Forum | Review | PDF | Favorites | |
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