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The geometry of Minkowski spaces - a survey. Part I

Martini, Horst, Swanepoel, Konrad and Weiss, Gunter (2001) The geometry of Minkowski spaces - a survey. Part I. Expositiones Mathematicae, 19 (2). pp. 97-142. ISSN 0723-0869

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Abstract

We survey elementary results in Minkowski spaces (i.e. finite dimensional Banach spaces) that deserve to be collected together, and give simple proofs for some of them. We place special emphasis on planar results. Many of these results have often been rediscovered as lemmas to other results. In Part I we cover the following topics: The triangle inequality and consequences such as the monotonicity lemma, geometric characterizations of strict convexity, normality (Birkhoff orthogonality), conjugate diameters and Radon curves, equilateral triangles and the affine regular hexagon construction, equilateral sets, circles: intersection, circumscribed, characterizations, circumference and area, inscribed equilateral polygons.

Item Type: Article
Official URL: http://shop.elsevier.de/expomath
Additional Information: © 2004 Elsevier
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 09:55
URL: http://eprints.lse.ac.uk/25401/

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