Minkowski Geometry—Some Concepts and Recent Developments

Vitor Balestro () and Horst Martini ()
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Vitor Balestro: Universidade Federal Fluminense, Instituto de Matemática e Estatística
Horst Martini: Technische Universität Chemnitz, Fakultät für Mathematik

Chapter Chapter 3 in Surveys in Geometry I, 2022, pp 49-95 from Springer

Abstract: Abstract The geometry of finite-dimensional normed spaces (= Minkowski geometry) is a research topic which is related to many other fields, such as convex geometry, discrete and computational geometry, subfields of functional analysis, Finsler geometry, and optimization. For that reason, Minkowski geometry is connected with a lot of interesting and recent research directions. The main objective of this exposition is to discuss some recent progress in various ramifications of the subject area, as well as to present some open problems and research directions. We also present brief historical overviews and some basic concepts of the theory.

Keywords: Angular measures; Birkhoff orthogonality; Curvature; Curvature types; Differential geometry; Distance geometry problem; Elementary geometry; Equilateral set; Fermat–Torricelli problem; Finsler geometry; Geometric constants; Hadwiger’s covering conjecture; Mahler’s conjecture; Minkowski billiards; Minkowski geometry; Normed spaces; Reduced bodies; Viterbo’s conjecture; 52A21; 52A10; 52A15; 52A20; 52A38; 52A40; 46B20; 46B85; 53A15; 53A35; 53B40 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/978-3-030-86695-2_3

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