Boundary behavior of invariant functions on planar domains

TL;DR

This paper investigates the detailed boundary behavior of invariant metrics like Caratheodory, Kobayashi, and Bergman on smooth planar domains, under various regularity conditions.

Contribution

It provides precise descriptions of how these invariant functions behave near boundary points, advancing understanding of complex analysis in planar domains.

Findings

Explicit boundary asymptotics for invariant metrics

Behavior characterized under different boundary regularity assumptions

Enhanced understanding of boundary geometry effects

Abstract

Precise behavior of the Caratheodory, Kobayashi and Bergman metrics and distances near smooth boundary points of domains in C is found under different assumptions of regularity.