Invariant valuations on star-shaped sets

DOI10.1006/aima.1997.1601zbMath0889.52007OpenAlexW2158546039MaRDI QIDQ677491

Daniel A. Klain

Publication date: 9 April 1997

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

Full work available at URL: https://doi.org/10.1006/aima.1997.1601

zbMATH Keywords

valuationsstar-shaped set

Mathematics Subject Classification ID

Mixed volumes and related topics in convex geometry (52A39) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items (40)

Rotation Invariant Valuations ⋮ Radial continuous valuations on star bodies ⋮ Moment-entropy inequalities. ⋮ Generalizations of the Busemann-Petty problem for sections of convex bodies ⋮ Real-valued valuations on Sobolev spaces ⋮ New higher-order equiaffine invariants ⋮ Radial continuous rotation invariant valuations on star bodies ⋮ The Centro-Affine Hadwiger Theorem ⋮ Laplace transforms and valuations ⋮ A characterization for compact sets in the space of fuzzy star-shaped numbers with \(L_p\) metric ⋮ Covariance matrices and valuations ⋮ Valuations on Orlicz spaces and \(L^\phi\)-star sets ⋮ Affine invariant points ⋮ Geometric valuation theory ⋮ Fisher information and matrix-valued valuations ⋮ New \(L_p\) affine isoperimetric inequalities ⋮ Geometric tomography and local stereology. ⋮ Ellipsoids and matrix-valued valuations ⋮ Rényi divergence and \(L_p\)-affine surface area for convex bodies ⋮ New affine measures of symmetry for convex bodies ⋮ Starshaped sets ⋮ Divergence for \(s\)-concave and log concave functions ⋮ Continuous valuations on the space of Lipschitz functions on the sphere ⋮ The dual Brunn-Minkowski theory for bounded Borel sets: dual affine quermassintegrals and inequalities ⋮ Valuations and Busemann-Petty type problems ⋮ $\mathrm {SL}(n)$-contravariant $L_p$-Minkowski valuations ⋮ Continuity and representation of valuations on star bodies ⋮ On star duality of mixed intersection bodies ⋮ Ranking star-shaped valued mappings with respect to shape variability ⋮ \(\mathrm{SL}(n)\) invariant valuations on polytopes ⋮ On the uniqueness of gravitational centre ⋮ Relative entropies for convex bodies ⋮ When do sections of different dimensions determine a convex body? ⋮ Radial Minkowski additive operators ⋮ Minkowski valuations ⋮ A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\) ⋮ Valuations on function spaces ⋮ Minkowski valuations on $L^{p}$-spaces ⋮ Valuations on polytopes containing the origin in their interiors ⋮ Projection bodies and valuations

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