Several problems on reduced spherical polygons of thickness less than π/2

Abstract

The present paper aims to solve some problems proposed by Lassak about the reduced spherical polygons. The main result is to show that the regular spherical n-gon has the minimal perimeter among all reduced spherical polygons of fixed thickness less than π/2 and with at most n vertices. In addition, we determine the maximal diameter of every reduced spherical polygons with a fixed thickness less than π/2. We also find the smallest spherical radius that contains every reduced spherical polygons with a fixed thickness less than π/2.