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arXiv · 2511.16240

On the Bergman Kernel of complex hyperbolic manifolds

Jingzhou Sun
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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.

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Jingzhou Sun. 2025-11-20. On the Bergman Kernel of complex hyperbolic manifolds. https://arxiv.org/abs/2511.16240

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