Asymptotic boundary behavior of the Bergman curvatures of a pseudoconvex domain

TL;DR

This paper develops a new method to estimate the boundary behavior of Bergman curvatures in pseudoconvex domains, establishing uniform lower bounds near the boundary without relying on kernel regularity.

Contribution

It introduces a novel approach for lower bound estimates of Bergman curvatures that does not depend on boundary kernel regularity, and proves uniform bounds for domains with constant Levi rank.

Findings

Established a lower bound estimate for Bergman curvatures near the boundary.

Proved the existence of a uniform lower bound for bisectional curvatures in certain pseudoconvex domains.

Abstract

We present a method of obtaining a lower bound estimate of the curvatures of the Bergman metric without using the regularity of the kernel function on the boundary. As an application, we prove the existence of an uniform lower bound of the bisectional curvatures of the Bergman metric of a smooth bounded pseudoconvex domain near the boundary with constant Levi rank.