English

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.

Keywords

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}
}
R2 v1 2026-07-01T07:47:02.191Z