On the extremal distance between two convex bodies

DOI10.1007/s11856-011-0044-2zbMath1229.52005OpenAlexW2026385148MaRDI QIDQ636023

Márton Naszódi, Carlos Hugo Jiménez

Publication date: 25 August 2011

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-011-0044-2

zbMATH Keywords

Banach-Mazur distancesimplexJohn's position of convex bodiessmooth convex body

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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Stability result for the extremal Gr\"unbaum distance between convex bodies ⋮ John's ellipsoid and the integral ratio of a log-concave function ⋮ A Quantitative Helly-Type Theorem: Containment in a Homothet ⋮ EXTREMAL BANACH–MAZUR DISTANCE BETWEEN A SYMMETRIC CONVEX BODY AND AN ARBITRARY CONVEX BODY ON THE PLANE

Cites Work

• Über die affine Exzentrizität konvexer Körper
• Approximation of convex bodies by centrally symmetric bodies
• The only convex body with extremal distance from the ball is the simplex
• Distances between non-symmetric convex bodies and the \(MM^*\)-estimate
• John's decomposition in the general case and applications
• John's theorem for an arbitrary pair of convex bodies
• John's decomposition of the identity in the non-convex case
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