A sharp Rogers and Shephard inequality for the $p$-difference body of planar convex bodies

DOI10.1090/S0002-9939-08-09209-5zbMath1143.52008arXivmath/0702102MaRDI QIDQ3508085

Chiara Bianchini, Andrea Colesanti

Publication date: 27 June 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702102

zbMATH Keywords

shadow systemsparallel chord movements\(L_p\) Brunn-Minkowski theory\(p\)-sumlinear parameter systemsRogers Shephard inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (10)

On Brunn-Minkowski type inequalities and overdetermined problem for \(p\)-capacity ⋮ The Brunn-Minkowski-Firey inequality for nonconvex sets ⋮ The Orlicz centroid inequality for star bodies ⋮ On Rogers–Shephard-type inequalities for the lattice point enumerator ⋮ Stability in the \(L_p\) Shephard problem ⋮ The Orlicz Brunn-Minkowski inequality ⋮ Asymmetric $L_p$-difference bodies ⋮ A sharp Rogers-Shephard type inequality for Orlicz-difference body of planar convex bodies ⋮ Orlicz projection bodies ⋮ Rogers and Shephard inequality for the Orlicz difference body

Cites Work

• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
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• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Shadow systems of convex sets
• Convex Bodies Associated with a Given Convex Body
• Some extremal problems for convex bodies
• Volume Inequalities forL_p‐Zonotopes
• Shadow Systems and Volumes of Polar Convex Bodies
• On the $L_{p}$-Minkowski problem
• On the reverse L ^p –busemann–petty centroid inequality
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