Functional analytic characterizations of classes of convex bodies

DOI10.1007/PL00004539zbMath0874.52001OpenAlexW4247264696MaRDI QIDQ2365059

Erwin Lutwak, Wolfgang Weil, Paul R. Goodey

Publication date: 4 November 1997

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174889

zbMATH Keywords

convex coneintersection bodymixed volumeszonoidspolar projection bodydual mixed volumes

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Ordered topological linear spaces, vector lattices (46A40)

Related Items (30)

Projection functions, area measures and the Alesker-Fourier transform ⋮ On intersection and mixed intersection bodies ⋮ Comparison of volumes of convex bodies in real, complex, and quaternionic spaces ⋮ \(L_{p}\)-Aleksandrov-Fenchel inequality ⋮ Spherical projections and centrally symmetric sets ⋮ The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry ⋮ On the Busemann-Petty problem\\ concerning central sections\\ of centrally symmetric convex bodies ⋮ \(L_p\)-mixed intersection bodies and star duality ⋮ Busemann-Petty problems for quasi \(L_p\) intersection bodies ⋮ \(q\)-dual mixed volumes and \(L_{p}\)-intersection bodies ⋮ On the average volume of sections of convex bodies ⋮ Comparison problems for Radon transforms ⋮ Intersection bodies and generalized cosine transforms ⋮ Starshaped sets ⋮ Sections of convex bodies with symmetries ⋮ Valuations and Busemann-Petty type problems ⋮ An example related to the slicing inequality for general measures ⋮ On mixed complex intersection bodies ⋮ \(L_{p}\)-Brunn-Minkowski inequality ⋮ Intersection Bodies and the Busemann-Petty Problem ⋮ Local properties of intertwining operators on the sphere ⋮ Inequalities for radial Blaschke–Minkowski homomorphisms ⋮ Brunn-Minkowski inequality for mixed intersection bodies ⋮ Affine isoperimetric inequalities for \(L_p\)-intersection bodies ⋮ Centered Bodies and Dual Mixed Volumes ⋮ Busemann-Petty problems for L_p mixed intersection bodies ⋮ A classification of some unit Lorentz balls as non-intersection bodies ⋮ \(L_{p}\)-mixed intersection bodies ⋮ The Busemann-Petty problem on entropy of log-concave functions ⋮ Convex intersection bodies in three and four dimensions

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