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

Stuart James Hall; Thomas Murphy

paper

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

arXiv:1308.1312

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.

11 pages v4 updated to reflect referee's comments; to appear in Ann. Global Anal. Geom

Bounding λ2​ for Kähler-Einstein metrics with large symmetry groups

Abstract

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