Year: 2020
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Guo, Bin, Phong, Duong H., Sturm, Jacob
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2999513327