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arXiv · 1702.07126

Lower bounds on the Bergman metric near points of infinite type

Dau The Phiet·Ninh Van Thu
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Abstract

Let $\Omega$ be a pseudoconvex domain in $\mathbb C^n$ satisfying an $f$-property for some function $f$. We show that the Bergman metric associated to $\Omega$ has the lower bound $\tilde g(\delta_\Omega(z)^{-1})$ where $\delta_\Omega(z)$ is the distance from $z$ to the boundary $\partial\Omega$ and $\tilde g$ is a specific function defined by $f$. This refines Khanh-Zampieri's work in \cite{KZ12} with reducing the smoothness assumption of the boundary.

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Dau The Phiet, Ninh Van Thu. 2017-02-23. Lower bounds on the Bergman metric near points of infinite type. https://arxiv.org/abs/1702.07126

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