Hilbert geometry for convex polygonal domains

TL;DR

This paper demonstrates that the Hilbert geometry on any open convex polygonal domain is Lipschitz equivalent to the Euclidean plane, establishing a fundamental geometric relationship.

Contribution

It proves the Lipschitz equivalence between Hilbert geometry on convex polygons and Euclidean geometry, a novel result in geometric analysis.

Findings

Hilbert geometry on convex polygons is Lipschitz equivalent to Euclidean plane

Establishes a fundamental geometric relationship for convex polygonal domains

Provides a basis for further geometric and metric analysis in convex domains

Abstract

We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane.