Reduced convex bodies in Euclidean space -- a survey

DOI10.1016/j.exmath.2011.01.006zbMath1213.52006OpenAlexW1974783611MaRDI QIDQ534169

Marek Lassak, Horst Martini

Publication date: 17 May 2011

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2011.01.006

zbMATH Keywords

thicknessdiameterconvex bodyconstant widthperimetercomplete setminimal widthisodiametric problemreduced bodywidth function

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Isoperimetric problems for polytopes (52B60) 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 (17)

Spherical Geometry—A Survey on Width and Thickness of Convex Bodies ⋮ Spherical bodies of constant width ⋮ On reduced triangles in normed planes ⋮ Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes ⋮ Complete sets and completion of sets in Banach spaces ⋮ Complete sets in normed linear spaces ⋮ Covering a reduced spherical polygon by a disk ⋮ The circumradius of planar reduced convex bodies ⋮ The perimeter and area of reduced spherical polygons of thickness \(\pi /2\) ⋮ Is a complete, reduced set necessarily of constant width? ⋮ Hunting for reduced polytopes ⋮ Approximation of Spherical Bodies of Constant Width and Reduced Bodies ⋮ Reduced convex bodies in finite dimensional normed spaces: a survey ⋮ Vertex-facet assignments for polytopes ⋮ Covering of a reduced spherical body by a disk ⋮ Complete sets need not be reduced in Minkowski spaces ⋮ Width of spherical convex bodies

Cites Work

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