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Absorbing angles, Steiner minimal trees and antipodality

Swanepoel, Konrad, 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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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
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 09 Oct 2009 09:53
URL: http://eprints.lse.ac.uk/25403/

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