Discrete sequences in unbounded domains

TL;DR

This paper investigates the behavior of discrete sequences in unbounded domains, showing that certain boundary escape estimations valid in bounded strongly pseudoconvex domains do not hold in unbounded cases.

Contribution

It extends the study of discrete sequences and boundary behavior from bounded to unbounded domains, highlighting the failure of previous estimations.

Findings

Boundary escape estimations fail in unbounded domains

Discrepancies between bounded and unbounded domain behaviors

Insights into Kobayashi distance in complex analysis

Abstract

Discrete sequences with respect to the Kobayashi distance in a strongly pseudoconvex bounded domain $D$ are related to Carleson measures by a formula that uses the Euclidean distance from the boundary of $D$. Thus the speed of escape at the boundary of such sequence has been studied in details for strongly pseudoconvex bounded domain $D$. In this note we show that such estimations completely fail if the domain is not bounded.