An Inequality for Sections and Projections of a Convex Set

DOI10.2307/2160081zbMath0779.52011OpenAlexW4243408428MaRDI QIDQ3134701

Jonathan E. Spingarn

Publication date: 13 September 1993

Full work available at URL: https://doi.org/10.2307/2160081

zbMATH Keywords

convex bodyquermassintegralsgeometric inequalities

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (13)

A geometric inequality and a low 𝑀-estimate ⋮ On minmax and maxmin inequalities for centered convex bodies ⋮ Affine invariant points ⋮ On a generalization of the Hermite-Hadamard inequality and applications in convex geometry ⋮ Small ball probability estimates for log-concave measures ⋮ Geometry of sets of quantum maps: A generic positive map acting on a high-dimensional system is not completely positive ⋮ A remark on the slicing problem ⋮ Convex geometry and waist inequalities ⋮ Small ball probability estimates, \(\psi_2\)-behavior and the hyperplane conjecture ⋮ Remarks on an inequality of Rogers and Shephard ⋮ Estimating the average of functions with convexity properties by means of a new center ⋮ Entropy and asymptotic geometry of non-symmetric convex bodies ⋮ On inner and outer radii in Minkowski spaces

Cites Work

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• Intersection bodies and dual mixed volumes
• Mean dual and harmonic cross-sectional measures
• Isoperimetric inequalities and identities for \(k\)-dimensional cross-sections of convex bodies
• Convex Bodies Associated with a Given Convex Body
• A Characterization of the n-Dimensional Parallelotope
• Inequalities for the Difference Body of a Convex Body
• Convex Analysis

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