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The geometry of Minkowski spaces – a survey. I. (English) Zbl 0984.52004
The authors give a survey over various aspects of the geometry of Minkowski spaces (finite-dimensional normed vector spaces), thus supplementing the excellent monograph by A. C. Thompson [Minkowski geometry, Cambridge (1996; Zbl 0868.52001)]. Much of the survey is restricted to the two-dimensional case, but there are also outlooks to higher dimensions. The authors provide a number of simplified or new proofs, and they have collected more than 200 references.
The following topics are covered: the triangle inequality and its 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, perimeter and area, inscribed equilateral polygons.

MSC:
52A21 Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)
52A10 Convex sets in \(2\) dimensions (including convex curves)
52-02 Research exposition (monographs, survey articles) pertaining to convex and discrete geometry
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