The unit ball is an attractor of the intersection body operator

DOI10.1016/j.aim.2010.07.018zbMath1215.44002OpenAlexW1967705800MaRDI QIDQ624333

Artem Zvavitch, Alexander Fish, Dmitri Ryabogin, F. L. Nazarov

Publication date: 9 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.aim.2010.07.018

zbMATH Keywords

Radon transformconvex bodyintersection bodyspherical Radon transform

Mathematics Subject Classification ID

Radon transform (44A12) Convex sets in (3) dimensions (including convex surfaces) (52A15) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items

A solution to the fifth and the eighth Busemann-Petty problems in a small neighborhood of the Euclidean ball ⋮ Iterations of the projection body operator and a remark on Petty's conjectured projection inequality ⋮ ITERATIONS OF CURVATURE IMAGES ⋮ The geometry of \(p\)-convex intersection bodies ⋮ Iterations of Minkowski valuations ⋮ A LOCAL UNIQUENESS THEOREM FOR MINIMIZERS OF PETTY's CONJECTURED PROJECTION INEQUALITY ⋮ Cyclic Brunn-Minkowski inequalities for dual mixed volumes ⋮ The second mixed projection problem and the projection centroid conjectures ⋮ General \((p,q)\)-mixed projection bodies ⋮ The (p, q)-mixed geominimal surface areas ⋮ The dual Orlicz-Brunn-Minkowski theory

Cites Work

• Intersection bodies and dual mixed volumes
• Topics in approximation theory
• Über die Projektionenkörper konvexer Polytope
• Convolutions, Transforms, and Convex Bodies
• A Theorem on Convex Bodies of the Brunn-Minkowski Type
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