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

Stuart James Hall; Thomas Murphy

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arXiv · 1308.1312

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

Stuart James Hall·Thomas Murphy

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Abstract

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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Stuart James Hall, Thomas Murphy. 2014-02-23. Bounding $λ_{2}$ for Kähler-Einstein metrics with large symmetry groups. https://arxiv.org/abs/1308.1312

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