# Hyperbolicity in unbounded convex domains

## TL;DR

This paper characterizes Kobayashi hyperbolicity in unbounded convex domains using various mathematical tools like peak functions, affine lines, and Bergman metrics, enhancing understanding of complex geometric structures.

## Contribution

It offers new equivalent characterizations of hyperbolicity in unbounded convex domains, connecting multiple mathematical concepts.

## Key findings

- Characterizations via peak and anti-peak functions at infinity
- Connections with affine lines and Bergman metric
- Implications for iteration theory in complex analysis

## Abstract

We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.