Kahler-Einstein Metrics and Eigenvalue Gaps
Differential Geometry
2020-01-17 v1
Abstract
The existence of Kahler-Einstein metrics on a Fano manifold is characterized in terms of a uniform gap between 0 and the first positive eigenvalue of the Cauchy-Riemann operator on smooth vector fields. It is also characterized by a similar gap between 0 and the first positive eigenvalue for Hamiltonian vector fields. The underlying tool is a compactness criterion for suitably bounded subsets of the space of Kahler potentials which implies a positive gap.
Cite
@article{arxiv.2001.05794,
title = {Kahler-Einstein Metrics and Eigenvalue Gaps},
author = {Bin Guo and Duong H. Phong and Jacob Sturm},
journal= {arXiv preprint arXiv:2001.05794},
year = {2020}
}