Convexity of \(L_p\)-intersection bodies

DOI10.1016/j.aim.2009.05.009zbMath1179.52005OpenAlexW1988445955MaRDI QIDQ843228

Gautier Berck

Publication date: 29 September 2009

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

Full work available at URL: https://doi.org/10.1016/j.aim.2009.05.009

zbMATH Keywords

intersection body\(L_p\)-intersection bodyBusemann's convexity theorem

Mathematics Subject Classification ID

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

Related Items (21)

Orlicz mixed chord-integrals ⋮ Orlicz-Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms ⋮ Counterexamples to convexity of $k$-intersection bodies ⋮ Orlicz mixed radial Blaschke-Minkowski homomorphisms ⋮ Complex \(L_p\)-intersection bodies ⋮ The multiple radial Blaschke-Minkowski homomorphisms ⋮ The geometry of \(p\)-convex intersection bodies ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ Radial Blaschke--Minkowski homomorphisms and volume differences ⋮ Orlicz mean dual affine quermassintegrals ⋮ Starshaped sets ⋮ A new proof of the Orlicz Busemann-Petty centroid inequality ⋮ The normalized L_p intersection bodies ⋮ Orlicz Version of Mixed Mean Dual Affifine Quermassintegrals ⋮ Determination of star bodies from \(p\)-centroid bodies ⋮ Local properties of intertwining operators on the sphere ⋮ Orlicz dual affine quermassintegrals ⋮ The logarithmic intersection body ⋮ Busemann-Petty problems for general \(L_p\)-intersection bodies ⋮ Volume sums of polar Blaschke-Minkowski homomorphisms ⋮ General \(L_{p}\)-dual Blaschke bodies and the applications

Cites Work

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• General \(L_{p}\) affine isoperimetric inequalities
• Intersection bodies and dual mixed volumes
• A positive solution to the Busemann-Petty problem in \(\mathbb{R}^4\)
• An analytic solution to the Busemann-Petty problem on sections of convex bodies
• Blaschke-Santaló inequalities
• The \(L^p\)-Busemann-Petty centroid inequality
• \(L_ p\) affine isoperimetric inequalities.
• A positive answer to the Busemann-Petty problem in three dimensions
• Intrinsic area
• Intersection bodies and valuations
• A characterization of Lp intersection bodies
• p-Cross-section bodies
• The Brunn-Minkowski inequality
• Centroid bodies and comparison of volumes
• A Theorem on Convex Bodies of the Brunn-Minkowski Type
• \(L_p\) intersection bodies

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