Three characterizations of reducedness of spherical convex polygons

Marek Lassak

Three characterizations of reducedness of spherical convex polygons

Metric Geometry 2025-09-17 v1

Authors: Marek Lassak

Abstract

Denote by $S^2$ the two-dimensional sphere. A spherical convex body on $S^2$ 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 $S^2$ . Analogous characterizations hold true also in the Euclidean and hyperbolic planes.

Keywords

spherical convex geometry reduced body spherical convex polygons spherical thickness convexity characterizations

Cite

@article{arxiv.2509.12427,
  title  = {Three characterizations of reducedness of spherical convex polygons},
  author = {Marek Lassak},
  journal= {arXiv preprint arXiv:2509.12427},
  year   = {2025}
}

Comments

7 pages, 1 figure

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