Reverse inequalities for zonoids and their application

DOI10.1016/j.aim.2011.07.018zbMath1230.52021OpenAlexW2043010349MaRDI QIDQ645213

Rolf Schneider, Daniel Hug

Publication date: 8 November 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2011.07.018

zbMATH Keywords

mixed volumezonoidisotropic measureassociated zonoidcharacterization of parallelepipedshyperplane processintersection densityreverse Urysohn inequality

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (16)

Reverse Alexandrov–Fenchel inequalities for zonoids ⋮ Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies ⋮ Volume inequalities for sections and projections of Wulff shapes and their polars ⋮ Vector-valued Maclaurin inequalities ⋮ Shadow systems of asymmetric \(L_p\) zonotopes ⋮ Weighted Brunn-Minkowski theory. I: On weighted surface area measures ⋮ Isoperimetric problems for zonotopes ⋮ Isomorphic versions of reverse isoperimetric inequalities ⋮ On a quantitative reversal of Alexandrov’s inequality ⋮ Volume inequalities for asymmetric Orlicz zonotopes ⋮ REMARKS ABOUT MIXED DISCRIMINANTS AND VOLUMES ⋮ Reverse and dual Loomis-Whitney-type inequalities ⋮ Strengthened inequalities for the mean width and the ℓ‐norm ⋮ Sharp inequalities related to the functional \(U_j\) and some applications ⋮ Intersection and proximity of processes of flats ⋮ Volume inequalities for complex isotropic measures

Cites Work

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• Über die affine Exzentrizität konvexer Körper
• On the Aleksandrov-Fenchel inequality involving zonoids
• Zonoide und verwandte Klassen konvexer Körper
• Isoperimetric inequalities for the mixed area of plane convex sets
• Centrally symmetric convex bodies and distributions. II
• Volume inequalities for subspaces of \(L_p\)
• Surface Area of a Convex Body Under Affine Transformations
• Extremum properties of the intersection densities of stationary poisson hyperplane processes
• Volume Ratios and a Reverse Isoperimetric Inequality
• Stochastic and Integral Geometry
• Zonoids with Minimal Volume-Product--A New Proof
• Shadows of Convex Bodies
• Hyperplans poissoniens et compacts de Steiner
• Finite dimensional subspaces of $L_{p}$

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