On the Kobayashi hyperbolicity of tube domains in ${\mathbb C}^2$

TL;DR

This paper presents a simple counterexample to a previously proposed criterion for determining Kobayashi hyperbolicity in certain tube domains in complex two-dimensional space, challenging existing assumptions.

Contribution

The authors provide an elementary counterexample that refutes a known criterion for Kobayashi hyperbolicity in a specific class of tube domains in ${ m C}^2$.

Findings

Counterexample disproves the criterion

Challenges previous assumptions about hyperbolicity

Refines understanding of Kobayashi hyperbolicity in tube domains

Abstract

We construct an elementary counterexample to the criterion for Kobayashi hyperbolicity for a class of tube domains in ${\mathbb C}^2$ proposed by J.-J. Loeb.