Maximum and minimum sets for some geometric mean values

DOI10.1007/BF01045156zbMath0715.60010MaRDI QIDQ751696

Richard E. Pfiefer

Publication date: 1990

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

zbMATH Keywords

minimal volumegeometric probabilityrandom simplexcharacterization of ellipsoids

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05)

Related Items (18)

Some conjectures aboutLp norms of k-plane transforms ⋮ Inequalities for integral means over symmetric sets ⋮ T-SNE, forceful colorings, and mean field limits ⋮ Some inequalities for chord power integrals of parallelotopes ⋮ A general rearrangement inequality ⋮ Sets that maximize probability and a related variational problem ⋮ Rearrangement inequalities of the one-dimensional maximal functions associated with general measures ⋮ Intersections of Poisson \(k\)-flats in constant curvature spaces ⋮ Sharp norm estimates for functional dual affine quermassintegrals ⋮ Geometric tomography and local stereology. ⋮ A probabilistic take on isoperimetric-type inequalities ⋮ Volume difference inequalities ⋮ The dual Brunn-Minkowski theory for bounded Borel sets: dual affine quermassintegrals and inequalities ⋮ Rearrangement inequalities with application to ratios of heat kernels ⋮ Sharp inequalities for the mean distance of random points in convex bodies ⋮ A convex body associated to the Busemann random simplex inequality and the Petty conjecture ⋮ Bounding marginal densities via affine isoperimetry ⋮ A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem

Cites Work

• On the average size of polytopes in a convex set
• Gewichtete Volumsmittelwerte von Simplices, welche zufällig in einem konvexen Körper des \(R^n\) gewählt werden
• On some mean values associated with a randomly selected simplex in a convex set
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• Random triangles in convex regions
• Random approximation of convex sets*
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
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