The geometry of Minkowski spaces – a survey. II. (English) Zbl 1080.52005
The authors continue their useful survey over various aspects of the geometry of Minkowski spaces (finite-dimensional Banach spaces). While the first part [Expo. Math. 19, No. 2, 97–142 (2001; Zbl 0984.52004)], written together with G. Weiß, was mainly restricted to two-dimensional spaces, this second part is devoted to higher dimensions. After a fairly complete survey over bodies of constant Minkowski width, the following topics are treated: generalized convexity notions of importance for Minkowski spaces (with \(d\)-convexity in the foreground), bisectors and Voronoi diagrams in Minkowski spaces.
This thoroughly prepared survey collects more than 300 references.
This thoroughly prepared survey collects more than 300 references.
Reviewer: Rolf Schneider (Freiburg i. Br.)
MSC:
| 52A21 | Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) |
| 46B20 | Geometry and structure of normed linear spaces |
| 52-02 | Research exposition (monographs, survey articles) pertaining to convex and discrete geometry |
| 52A01 | Axiomatic and generalized convexity |
Keywords:
Minkowski geometry; Minkowski space; finite-dimensional normed space; bodies of constant width; generalized convexity; bisector; Voronoi diagramCitations:
Zbl 0984.52004Software:
VoronoiReferences:
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