Estimates of invariant metrics on pseudoconvex domains near boundaries with constant Levi ranks

TL;DR

This paper provides estimates for the Bergman kernel and metrics on pseudoconvex domains near boundaries with constant Levi ranks, advancing understanding of their boundary behavior.

Contribution

It introduces new estimates for invariant metrics on pseudoconvex domains with constant Levi ranks near their boundaries.

Findings

Derived bounds for the Bergman kernel near boundary points.

Established estimates for Bergman and Kobayashi metrics.

Enhanced understanding of boundary regularity effects.

Abstract

Estimates of the Bergman kernel and the Bergman and Kobayashi metrics on pseudoconvex domains near boundaries with constant Levi ranks are given.