On the Bergman metric of a pseudoconvex domain with a strongly pseudoconvex polyhedral boundary point

TL;DR

This paper investigates the Bergman metric on certain complex domains with non-smooth boundary points and demonstrates that it does not satisfy Einstein's condition, highlighting geometric limitations.

Contribution

It provides a novel analysis of the Bergman metric's properties near non-smooth boundary points in pseudoconvex domains, showing it is not Einstein.

Findings

Bergman metric is not Einstein near non-smooth boundary points

Analysis applies to unbounded pseudoconvex domains

Highlights geometric constraints of the Bergman metric

Abstract

Let $D\subset\mathbb{C}^n$ with $n>1$ be a pseudoconvex domain, possibly unbounded, that contains a non-smooth strongly pseudoconvex polyhedral boundary point. We show that the Bergman metric of $D$ is not Einstein.