Estimates of the Bergman distance on Dini-smooth bounded planar domains

TL;DR

This paper provides precise estimates for the Bergman distance on Dini-smooth bounded planar domains, demonstrating that it closely aligns with the Carathéodory and Kobayashi distances, thus enhancing understanding of their relationships.

Contribution

The paper introduces new precise estimates for the Bergman distance on Dini-smooth bounded planar domains, showing its near equivalence to other intrinsic distances.

Findings

Bergman distance estimates are refined for Dini-smooth domains.

Bergman, Carathéodory, and Kobayashi distances nearly coincide on these domains.

The results improve understanding of intrinsic metrics in complex analysis.

Abstract

Precise estimates for the Bergman distances of Dini-smooth bounded planar domains are given. These estimates imply that on such domains the Bergman distance almost coincides with the Carath\'eodory and Kobayashi distances.