For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere we consider the width of C determined by K. By the thickness Δ(C) of C we mean the minimum of the widths of C over all supporting hemispheres K of C. A spherically convex body is said to be reduced provided Δ(Z) < Δ(R) for every spherically convex body Z ⊂ R different from R. We characterize reduced spherical polygons on S². We show that every reduced spherical polygon is of thickness at most π/2. We also estimate the diameter of reduced spherical polygons in terms of their thickness. Moreover, a few other properties of reduced spherical polygons are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-5,
author = {Marek Lassak},
title = {Reduced spherical polygons},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {205-216},
zbl = {1316.52017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-5}
}
Marek Lassak. Reduced spherical polygons. Colloquium Mathematicae, Tome 139 (2015) pp. 205-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-5/