A countable set of directions is sufficient for Steiner symmetrization

DOI10.1016/j.aam.2011.04.005zbMath1230.52007arXiv1105.0400OpenAlexW2125898931MaRDI QIDQ720599

Gaoyong Zhang, Erwin Lutwak, Gabriele Bianchi, Deane Yang, Daniel A. Klain

Publication date: 11 October 2011

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

Full work available at URL: https://arxiv.org/abs/1105.0400

zbMATH Keywords

convex bodySteiner symmetrization

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (14)

Generalization of Klain’s theorem to Minkowski symmetrization of compact sets and related topics ⋮ On iterations of Steiner symmetrizations ⋮ Random Symmetrizations of Convex Bodies ⋮ Convergence of symmetrization processes ⋮ Smoothness of the Steiner symmetrization ⋮ Random polarizations ⋮ Steiner symmetrization using a finite set of directions ⋮ Lipschitz star bodies ⋮ Random Steiner symmetrizations of sets and functions ⋮ Convergence properties of symmetrization processes ⋮ A new approach to Steiner symmetrization of coercive convex functions ⋮ Steiner symmetrization \((n-1)\) times is sufficient to transform an ellipsoid to a ball in \(\mathbb{R}^n\) ⋮ Orlicz projection bodies ⋮ Minkowski symmetrization and projection bodies

Cites Work

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• The perimeter inequality under Steiner symmetrization: cases of equality
• Approximation of symmetrizations and symmetry of critical points
• General \(L_{p}\) affine isoperimetric inequalities
• Orlicz projection bodies
• Symmetrals and X-rays of planar convex bodies
• An isoperimetric inequality for convex polygons and convex sets with the same symmetrals
• Planar rectangular sets and Steiner symmetrization
• Steiner symmetrization is continuous in \(W^{1,p}\)
• Isomorphic Steiner symmetrization
• Steiner symmetrals and their distance from a ball
• Steiner symmetric extremals in Pólya-Szegő-type inequalities
• Partial Steiner symmetrization and some conduction problems
• A Result on the Steiner Symmetrization of a Compact Set
• The Brunn-Minkowski inequality
• Convex and Discrete Geometry
• Universal approximation of symmetrizations by polarizations
• Rapid Steiner Symmetrization of Most of a Convex Body and the Slicing Problem

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