Cookies?
Library Header Image
LSE Research Online LSE Library Services

Absorbing angles, Steiner minimal trees and antipodality

Swanepoel, Konrad and 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

Full text not available from this repository.
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
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 09 Oct 2009 09:53
Last Modified: 01 Oct 2010 09:27
URI: http://eprints.lse.ac.uk/id/eprint/25403

Actions (login required)

View Item View Item