The Brunn-Minkowski-Firey inequality for nonconvex sets

DOI10.1016/j.aam.2011.11.003zbMath1252.52006OpenAlexW2065830706MaRDI QIDQ408126

Deane Yang, Gaoyong Zhang, Erwin Lutwak

Publication date: 29 March 2012

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

Full work available at URL: https://doi.org/10.1016/j.aam.2011.11.003

zbMATH Keywords

Brunn-Minkowski inequalityBrunn-Minkowski-Firey inequalityMinkowski combinationsMinkowski-Firey \(L_p\)-combinations

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40)

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Cites Work

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• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Sharp convex Lorentz-Sobolev inequalities
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Concentration of mass on convex bodies
• General affine surface areas
• General \(L_{p}\) affine isoperimetric inequalities
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• Ellipsoids and matrix-valued valuations
• On the \(p\)-affine surface area
• The \(L^p\)-Busemann-Petty centroid inequality
• The discrete planar \(L_0\)-Minkowski problem
• \(L_ p\) affine isoperimetric inequalities.
• Sharp affine \(L_ p\) Sobolev inequalities.
• Positions of convex bodies associated to extremal problems and isotropic measures
• Valuations on polytopes containing the origin in their interiors
• Projection bodies and valuations
• Surface bodies and \(p\)-affine surface area
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• On the regularity of solutions to a generalization of the Minkowski problem
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Small ball probability estimates, \(\psi_2\)-behavior and the hyperplane conjecture
• A stability result for mean width of \(L_{p}\)-centroid bodies
• Asymmetric affine \(L_p\) Sobolev inequalities
• New \(L_p\) affine isoperimetric inequalities
• Volume inequalities for subspaces of \(L_p\)
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Intersection bodies and valuations
• A characterization of Lp intersection bodies
• A sharp Rogers and Shephard inequality for the $p$-difference body of planar convex bodies
• Star body valued valuations
• The Brunn-Minkowski inequality
• $L_p$ John Ellipsoids
• Fourier transform and Firey projections of convex bodies
• Small ball probability estimates for log-concave measures
• On $L_p$-affine surface areas
• Minkowski valuations
• Centroid bodies and comparison of volumes
• $p$-Means of Convex Bodies.
• \(L_p\) intersection bodies

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