Reduced spherical polygons

• Autorzy: Marek Lassak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 52A10: Convex sets in 2 dimensions (including convex curves)
• 52A55: Spherical and hyperbolic convexity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 138
• Numer: 2
• Strony: 205-216

Daty

wydano

2015

Twórcy

autor

Marek Lassak

• Institute of Mathematics and Physics, University of Science and Technology, 85-789 Bydgoszcz, Poland

Identyfikatory

DOI

10.4064/cm138-2-5