Asymptotic behaviour of the Bergman kernel and metric

Ravi Shankar Jaiswal

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arXiv · 2311.01097

Asymptotic behaviour of the Bergman kernel and metric

Ravi Shankar Jaiswal

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Abstract

We prove nontangential asymptotic limits of the Bergman kernel on the diagonal, and the Bergman metric and its holomorphic sectional curvature at exponentially flat infinite type boundary points of smooth bounded pseudoconvex domains in $\mathbb{C}^{n+1}$, $n\in\mathbb{N}$. We first show that these objects satisfy appropriate localizations and then use the method of scaling to complete the proof.

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Ravi Shankar Jaiswal. 2023-11-02. Asymptotic behaviour of the Bergman kernel and metric. https://arxiv.org/abs/2311.01097

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