Three characterizations of reducedness of spherical convex polygons

2025/09/15 by Lassak, Marek
#52A55 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2509.12427

Abstract

Denote by S² the two-dimensional sphere. A spherical convex body on S² which does not properly contain a spherical convex body of the same spherical thickness is called a reduced body. We give three characterizations of reducedness of spherical convex odd-gons on S². Analogous characterizations hold true also in the Euclidean and hyperbolic planes.

Citations

• Approximation of spherical convex bodies of constant width π/2
• Reduced polygons in the hyperbolic plane
• Spherical geometry -- a survey on width and thickness of convex bodies
• Reduced Spherical Convex Bodies

Related

• Reduced Spherical Convex Bodies
• On reduced spherical bodies
• Spherical geometry -- a survey on width and thickness of convex bodies
• Reduced polygons in the hyperbolic plane
• Covering a reduced spherical body by a disk