Structure of the space of diametrically complete sets in a Minkowski space

DOI10.1007/s00454-011-9393-1zbMath1259.52003OpenAlexW2084304984MaRDI QIDQ452002

José Pedro Moreno, Rolf Schneider

Publication date: 19 September 2012

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-011-9393-1

zbMATH Keywords

Minkowski spacepolyhedral normpolytopal complexset of constant widthdiametrically complete setextreme diametrically complete set

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (9)

Borsuk's partition problem in ℓₚ⁴ ⋮ Ball convex bodies in Minkowski spaces ⋮ Complete sets in normed linear spaces ⋮ Successive radii and ball operators in generalized Minkowski spaces ⋮ Some geometry of convex bodies in \(C(K)\) spaces ⋮ Is a complete, reduced set necessarily of constant width? ⋮ Schauder bases and diametrically complete sets with empty interior ⋮ The asymmetry of complete and constant width bodies in general normed spaces and the Jung constant ⋮ Complete sets need not be reduced in Minkowski spaces

Cites Work

• Diametrically complete sets in Minkowski spaces
• Meissner's mysterious bodies
• On complete convex bodies
• The extreme bodies in the set of plane convex bodies with a given width function
• Representations of polytopes and polyhedral sets
• Sets of constant width in finite dimensional Banach spaces
• The geometry of Minkowski spaces -- a survey. II.
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