Is a complete, reduced set necessarily of constant width?

DOI10.1515/advgeom-2017-0058zbMath1428.52004arXiv1602.07531OpenAlexW2963941953MaRDI QIDQ1737114

René Brandenberg, Bernardo González Merino, Horst Martini, Thomas Jahn

Publication date: 26 March 2019

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.07531

zbMATH Keywords

normed spacesgaugesbodies of constant widthgeneralized Minkowski spacesBohnenblust's inequalitycomplete bodiesLeichtweiss' inequalityperfect normsreduced bodies

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Geometry and structure of normed linear spaces (46B20) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (6)

Duality of gauges and symplectic forms in vector spaces ⋮ Minkowski Geometry—Some Concepts and Recent Developments ⋮ Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio ⋮ Complete sets in normed linear spaces ⋮ Tightening and reversing the arithmetic-harmonic mean inequality for symmetrizations of convex sets ⋮ Asymmetry measures for convex distance functions

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