The geometry of Minkowski spaces -- a survey. Part I

Details The geometry of Minkowski spaces -- a survey. Part I The geometry of Minkowski spaces -- a survey. Part I

2007-08-21

arxiv.org/abs/0708.2900v1

Expositiones Mathematicae 19 (2001) 97-142

Mathematics

Metric Geometry

56 pages, 28 figures

Scientific paper

10.1016/S0723-0869(01)80025-6

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.

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