Bounding $\lambda_{2}$ for K\"ahler-Einstein metrics with large symmetry groups
Differential Geometry
2014-02-25 v4
Abstract
We calculate an upper bound for the second nonzero eigenvalue of the scalar Laplacian, , for toric K\"ahler-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.
Cite
@article{arxiv.1308.1312,
title = {Bounding $\lambda_{2}$ for K\"ahler-Einstein metrics with large symmetry groups},
author = {Stuart James Hall and Thomas Murphy},
journal= {arXiv preprint arXiv:1308.1312},
year = {2014}
}
Comments
11 pages v4 updated to reflect referee's comments; to appear in Ann. Global Anal. Geom