Bergman and Caratheodory metrics of the Kohn-Nirenberg domains

TL;DR

This paper investigates the Bergman and Caratheodory metrics on Kohn-Nirenberg domains, showing they are both positive and complete, thereby advancing understanding of these complex unbounded domains.

Contribution

The paper proves that the Bergman and Caratheodory metrics on Kohn-Nirenberg domains are positive and complete, addressing key open questions in complex analysis.

Findings

Metrics are positive on Kohn-Nirenberg domains

Metrics are complete on these domains

Advances understanding of unbounded complex domains

Abstract

The Kohn-Nireberg domains are unbounded domains in the complex Euclidean space of dimension 2 upon which many outstanding questions are yet to be explored. The primary aim of this article is to demonstrate that the Bergman and Caratheodory metrics of any Kohn-Nirenberg domains are positive and complete.