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Absorbing angles, Steiner minimal trees and antipodality

Swanepoel, Konrad ORCID: 0000-0002-1668-887X, Martini, Horst and Oloff de Wet, P. (2009) Absorbing angles, Steiner minimal trees and antipodality. Journal of Optimization Theory and Applications, 143 (1). pp. 149-157. ISSN 0022-3239

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Identification Number: 10.1007/s10957-009-9552-1

Abstract

We give a new proof that a star {op i :i=1,…,k} in a normed plane is a Steiner minimal tree of vertices {o,p 1,…,p k } if and only if all angles formed by the edges at o are absorbing (Swanepoel in Networks 36: 104–113, 2000). The proof is simpler and yet more conceptual than the original one. We also find a new sufficient condition for higher-dimensional normed spaces to share this characterization. In particular, a star {op i :i=1,…,k} in any CL-space is a Steiner minimal tree of vertices {o,p 1,…,p k } if and only if all angles are absorbing, which in turn holds if and only if all distances between the normalizations equal 2. CL-spaces include the mixed ℓ 1 and ℓ ∞ sum of finitely many copies of ℝ.

Item Type: Article
Official URL: http://www.springer.com/math/journal/10957
Additional Information: © 2009 Springer
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 09 Oct 2009 09:53
Last Modified: 20 Jun 2021 01:41
URI: http://eprints.lse.ac.uk/id/eprint/25403

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