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
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: | 11 Dec 2024 23:29 |
| URI: | http://eprints.lse.ac.uk/id/eprint/25403 |
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