Kobayashi hyperbolic convex domains not biholomorphic to bounded convex domains

TL;DR

This paper constructs convex domains that are biholomorphic to bounded domains but are not bounded convex, revealing an obstruction linked to Gromov hyperbolicity of the Kobayashi metric.

Contribution

It introduces a novel method to distinguish convex domains based on Gromov hyperbolicity, showing they can be biholomorphic to bounded domains without being bounded convex.

Findings

Convex domains biholomorphic to bounded domains can lack bounded convexity.

Gromov hyperbolicity of the Kobayashi metric serves as an obstruction.

New examples of convex domains with specific biholomorphic properties.

Abstract

We construct families of convex domains that are biholomorphic to bounded domains, but not bounded convex domains. This is accomplished by finding an obstruction related to the Gromov hyperbolicity of the Kobayashi metric.