Firey-Shephard problems for homogeneous measures

DOI10.1016/j.jmaa.2017.08.054zbMath1381.52008OpenAlexW2753122391MaRDI QIDQ1674368

Denghui Wu

Publication date: 2 November 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.08.054

zbMATH Keywords

measuresFourier transformconvex bodies\(L_p\)-projection bodyFirey-Shephard problem

Mathematics Subject Classification ID

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

Related Items (6)

Existence of solution for Lp-Minkowski problem of 0 < p < 1 with measures in ℝn ⋮ The measure-comparison problem for polar \((p, \mu)\)-centroid bodies ⋮ \((p, q)\)-John ellipsoids ⋮ The isomorphic Busemann-Petty problem for \(s\)-concave measures ⋮ A variant of the \(L_p\)-Shephard problem via \((p,q)\)-projection bodies ⋮ The \(L_p\) John ellipsoids for general measures

Cites Work

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• \(L_ p\) affine isoperimetric inequalities.
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• Projections of convex bodies and the Fourier transform
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• An isomorphic version of the Busemann-Petty problem for arbitrary measures
• An extension of Minkowski's theorem and its applications to questions about projections for measures
• A generalization of \(L_{p}\)-Brunn-Minkowski inequalities and \(L_{p}\)-Minkowski problems for measures
• Shadow systems of convex sets
• Zu einem Problem von Shephard über die Projektionen konvexer Körper
• Fourier transform and Firey projections of convex bodies
• Convex Bodies The Brunn-MinkowskiTheory
• $p$-Means of Convex Bodies.

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