Steiner Ratio for Manifolds
Metric Geometry
2011-01-18 v1
Abstract
The Steiner ratio characterizes the greatest possible deviation of the length of a minimal spanning tree from the length of the minimal Steiner tree. In this paper, estimates of the Steiner ratio on Riemannian manifolds are obtained. As a corollary, the Steiner ratio for flat tori, flat Klein bottles, and projective plane of constant positive curvature are computed. Steiner ratio - Steiner problem - Gilbert--Pollack conjecture - surfaces of constant curvature
Keywords
Cite
@article{arxiv.1101.3144,
title = {Steiner Ratio for Manifolds},
author = {D. Cieslik and A. O. Ivanov and A. A. Tuzhilin},
journal= {arXiv preprint arXiv:1101.3144},
year = {2011}
}
Comments
11 pages