On the inverse Klain map

DOI10.1215/00127094-2333971zbMath1280.52003arXiv1206.5370OpenAlexW1984395793MaRDI QIDQ364190

Thomas Wannerer, Lukas Parapatits

Publication date: 5 September 2013

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.5370

zbMATH Keywords

polytopecontinuous monotone positive Minkowski valuationKlain mapMcMullen decompositionvaluations on convex bodies

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Dissections and valuations (Hilbert's third problem, etc.) (52B45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (22)

Structures on Valuations ⋮ A Hadwiger-Type Theorem for General Tensor Valuations ⋮ Projection functions, area measures and the Alesker-Fourier transform ⋮ Minkowski endomorphisms ⋮ A valuation-theoretic approach to translative-equidecomposability ⋮ Extremum of geometric functionals involving general \(L_{p}\)-projection bodies ⋮ Minkowski valuations under volume constraints ⋮ Lutwak-Petty projection inequalities for Minkowski valuations and their duals ⋮ Floating functions ⋮ On the extendability by continuity of angular valuations on polytopes ⋮ The Steiner formula for Minkowski valuations ⋮ Minkowski additive operators under volume constraints ⋮ Log-concavity properties of Minkowski valuations ⋮ Positivity of valuations on convex bodies and invariant valuations by linear actions ⋮ Minkowski valuations on lattice polytopes ⋮ Difference bodies in complex vector spaces ⋮ Integral geometry of unitary area measures ⋮ Aleksandrov-Fenchel inequalities for unitary valuations of degree 2 and 3 ⋮ Some inequalities on general \(L_p\)-mixed brightness integrals ⋮ Affine vs. Euclidean isoperimetric inequalities ⋮ Volume sums of polar Blaschke-Minkowski homomorphisms ⋮ General \(L_{p}\)-mixed-brightness integrals

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