Diameter, width and thickness in the hyperbolic plane

TL;DR

This paper introduces a new way to measure the width and thickness of convex bodies in the hyperbolic plane, compares it with existing concepts, and explores properties of bodies with constant width, diameter, and specified thickness.

Contribution

It proposes a novel measurement concept for convex bodies in hyperbolic geometry and analyzes its implications for bodies with constant width, diameter, and fixed thickness.

Findings

Comparison of new and existing width and thickness concepts

Results on bodies of constant width in hyperbolic plane

Results on bodies of constant diameter and given thickness

Abstract

This paper contains a new concept to measure the width and thickness of a convex body in the hyperbolic plane. We compare the known concepts with the new one and prove some results on bodies of constant width, constant diameter and given thickness.