Hilbert geometry of polytopes

TL;DR

This paper proves that the Hilbert metric on the interior of a convex polytope is bilipschitz equivalent to a normed vector space of the same dimension, revealing a geometric similarity.

Contribution

It establishes a bilipschitz equivalence between Hilbert geometry on polytopes and normed vector spaces, providing new insights into their geometric structure.

Findings

Hilbert metric on polytopes is bilipschitz to a normed space

The geometric structure of polytopes under Hilbert metric is similar to Euclidean spaces

Provides a foundation for further geometric analysis of polytopes

Abstract

It is shown that the Hilbert metric on the interior of a convex polytope is bilipschitz to a normed vector space of the same dimension.