On minimal Besicovitch arrangements

TL;DR

This paper investigates minimal Besicovitch arrangements, revealing their properties through probabilistic methods, establishing key equalities and inequalities, and connecting them to line arrangements in the plane.

Contribution

It introduces a probabilistic framework to analyze minimal Besicovitch arrangements, deriving new equalities and inequalities, and linking these arrangements to geometric line configurations.

Findings

Derived elegant equalities for minimal Besicovitch arrangements

Established inequalities related to arrangement properties

Connected arrangements to line configurations in R2

Abstract

In this paper we focus on minimal Besicovitch arrangements to highlight some of their properties. An appropriate probability space enables us to find again in an elegant way some straightforward equalities associated with these arrangements. Resulting inequalities are also brought out. A connection with arrangements of lines in R2 is eventually made, where possible.