Affine diameters of convex bodies -- a survey

DOI10.1016/j.exmath.2005.01.019zbMath1076.52001OpenAlexW2078735418MaRDI QIDQ556417

Valeriu Soltan

Publication date: 13 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.exmath.2005.01.019

zbMATH Keywords

conjugate diametersaffine diametermeasure of symmetrycritical ratio

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Other problems of combinatorial convexity (52A37) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (26)

Bisecting envelopes of convex polygons ⋮ Covering the boundary of a convex body with its smaller homothetic copies ⋮ Affine diameters of a convex body ⋮ Introducing symplectic billiards ⋮ The Fermat-Torricelli theorem in convex geometry ⋮ Dual mean Minkowski measures and the Grünbaum conjecture for affine diameters ⋮ Affine cross-polytopes inscribed in a convex body ⋮ Complete sets in normed linear spaces ⋮ Extreme area and perimeter bisectors in a triangle ⋮ Estimations of covering functionals of simplices ⋮ A branch-and-bound approach for estimating covering functionals of convex bodies ⋮ On the Pełczyński conjecture on Auerbach bases ⋮ Minimal simplices inscribed in a convex body ⋮ Covering functionals of Minkowski sums and direct sums of convex bodies ⋮ Characteristic properties of ellipsoids and convex quadrics ⋮ Homothetic covering of convex hulls of compact convex sets ⋮ Covering functionals of convex polytopes ⋮ Asymmetry measures for convex distance functions ⋮ Covering a convex body vs. covering the set of its extreme points ⋮ Affine diameters of convex bodies ⋮ Coproximinality of linear subspaces in generalized Minkowski spaces ⋮ Diameter, width and thickness in the hyperbolic plane ⋮ Orthogonality in Generalized Minkowski Spaces ⋮ On convex bodies that are characterizable by volume function. ``Old and recent problems for a new generation: a survey ⋮ On the illumination of a class of convex bodies ⋮ The classification of convex polygons with triangular area or perimeter bisecting deltoids

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