On the area of ordinary hyperbolic reduced polygons

Abstract

A convex body $R$ in the hyperbolic plane is reduced if any convex body $K\subset R$ has a smaller minimal width than $R$. We examine the area of a family of hyperbolic reduced $n$-gons, and prove that, within this family, regular $n$-gons have maximal area.

arXiv comment9 pages, 1 figure