The horofunction boundary and isometry group of the Hilbert geometry

TL;DR

This paper explicitly describes the horofunction boundary of Hilbert geometry and explores its application in analyzing the space's isometry group, contributing to the understanding of geometric compactifications.

Contribution

It provides an explicit description of the horofunction boundary for Hilbert geometry and demonstrates its use in studying the isometry group of the space.

Findings

Explicit characterization of the horofunction boundary.

Insights into the structure of the isometry group.

Potential applications in geometric analysis.

Abstract

The horofunction boundary is a means of compactifying metric spaces that was introduced by Gromov in the 1970s. We describe explicitly the horofunction boundary of the Hilbert geometry, and sketch how it may be used to study the isometry group of this space.