Valuations on polytopes containing the origin in their interiors

DOI10.1006/aima.2002.2077zbMath1015.52012OpenAlexW1973609573MaRDI QIDQ1851240

Monika Ludwig

Publication date: 16 December 2002

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

Full work available at URL: https://semanticscholar.org/paper/8e96b8c14b5b5b3416a7ec5960ef8edca46b6a4f

zbMATH Keywords

valuationHadwiger's characterization theorem

Mathematics Subject Classification ID

Dissections and valuations (Hilbert's third problem, etc.) (52B45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (30)

A Hadwiger-Type Theorem for General Tensor Valuations ⋮ Valuations on Lattice Polytopes ⋮ A valuation-theoretic approach to translative-equidecomposability ⋮ \(L_p\) Minkowski problem with not necessarily positive data ⋮ \(\mathrm{SL}(n)\) contravariant vector valuations ⋮ The Centro-Affine Hadwiger Theorem ⋮ Tensor valuations on lattice polytopes ⋮ Geometric valuation theory ⋮ The Brunn-Minkowski-Firey inequality for nonconvex sets ⋮ The Orlicz centroid inequality for star bodies ⋮ A characterization of the star duality mapping ⋮ Ellipsoids and matrix-valued valuations ⋮ The generalization of Minkowski problems for polytopes ⋮ Volume, polar volume and Euler characteristic for convex functions ⋮ The log-Brunn-Minkowski inequality ⋮ The Orlicz Brunn-Minkowski inequality ⋮ \(\mathrm{SL}(n)\) contravariant \(L_p\) harmonic valuations on polytopes ⋮ Invariant Valuations on Super-Coercive Convex Functions ⋮ \(\mathrm{SL}(n)\) covariant vector-valued valuations on \(L^p\)-spaces ⋮ $\mathrm {SL}(n)$-contravariant $L_p$-Minkowski valuations ⋮ SL(n)-covariantL_p-Minkowski valuations ⋮ \(\mathrm{SL}(n)\) invariant valuations on polytopes ⋮ Centro-affine tensor valuations ⋮ General affine surface areas ⋮ The even Orlicz Minkowski problem ⋮ Crofton measures and Minkowski valuations ⋮ SL($n$) covariant vector valuations on polytopes ⋮ Orlicz projection bodies ⋮ LYZ Matrices and SL() Contravariant Valuations on Polytopes ⋮ \(L_p\)-Minkowski valuations on \(L^q\)-spaces

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