On the Bergman Kernel of complex hyperbolic manifolds
Differential Geometry
2026-04-14 v3 Algebraic Geometry
Complex Variables
Abstract
We prove a formula for the Bergman kernel of polarized complex hyperbolic manifolds. The formula expresses the Bergman kernel as a sum over the geodesic loops in the manifold. As an application, we prove a result about the maximum and minimum of the Bergman kernel function. We also prove an estimate of the off-diagonal Bergman kernel.
Cite
@article{arxiv.2511.16240,
title = {On the Bergman Kernel of complex hyperbolic manifolds},
author = {Jingzhou Sun},
journal= {arXiv preprint arXiv:2511.16240},
year = {2026}
}