Reduced spherical polygons

@article{MarekLassak2015,
abstract = {For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere $S^\{d\}$ 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 $R ⊂ S^\{d\}$ 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.},
author = {Marek Lassak},
journal = {Colloquium Mathematicae},
keywords = {sphere; reduced body; spherically convex body; spherically convex polygon; width; thickness; diameter},
language = {eng},
number = {2},
pages = {205-216},
title = {Reduced spherical polygons},
url = {http://eudml.org/doc/284133},
volume = {138},
year = {2015},
}

TY - JOUR
AU - Marek Lassak
TI - Reduced spherical polygons
JO - Colloquium Mathematicae
PY - 2015
VL - 138
IS - 2
SP - 205
EP - 216
AB - For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere $S^{d}$ 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 $R ⊂ S^{d}$ 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.
LA - eng
KW - sphere; reduced body; spherically convex body; spherically convex polygon; width; thickness; diameter
UR - http://eudml.org/doc/284133
ER -