Asymmetry of convex polytopes and vertex index of symmetric convex bodies

DOI10.1007/s00454-008-9075-9zbMath1161.52008OpenAlexW2064896804MaRDI QIDQ1006390

Alexander E. Litvak, Efim D. Gluskin

Publication date: 24 March 2009

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

Full work available at URL: https://doi.org/10.1007/s00454-008-9075-9

zbMATH Keywords

illumination parametermeasures of symmetryasymmetry of polytopespolytopes with few verticesvertex index

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Local theory of Banach spaces (46B07) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Inequalities and extremum problems in real or complex geometry (51M16) Symmetry properties of polytopes (52B15)

Related Items (5)

On the vertex index of convex bodies ⋮ Approximations of convex bodies by measure-generated sets ⋮ Volume ratios for Cartesian products of convex bodies ⋮ Random approximation and the vertex index of convex bodies ⋮ On the symmetric average of a convex body

Cites Work

• Combinatorial problems on the illumination of convex bodies
• On the asymmetry constant of a body with few vertices
• On the vertex index of convex bodies
• The illumination conjecture and its extensions
• A Sufficient Condition for an Integral Operator to Have a Trace.
• Inequalities between the Two Kinds of Eigenvalues of a Linear Transformation
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