Bounding $λ_{2}$ for Kähler-Einstein metrics with large symmetry groups

preprint2014arXivOpen access

We calculate an upper bound for the second nonzero eigenvalue of the scalar Laplacian, $λ_{2}$ , for toric Kähler-Einstein metrics in terms of the polytope data. We give some detailed examples in complex dimensions 1, 2 and 3. We also discuss extensions of this method to other geometries.

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Bounding $λ_{2}$ for Kähler-Einstein metrics with large symmetry groups

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Bounding λ2λ_{2}λ2​ for Kähler-Einstein metrics with large symmetry groups

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Bounding $λ_{2}$ for Kähler-Einstein metrics with large symmetry groups