Steiner symmetrization using a finite set of directions

DOI10.1016/j.aam.2011.09.004zbMath1244.52007arXiv1105.0868OpenAlexW2153908631MaRDI QIDQ408120

Daniel A. Klain

Publication date: 29 March 2012

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

Full work available at URL: https://arxiv.org/abs/1105.0868

zbMATH Keywords

convex bodySteiner symmetrizationBlaschke selection theoremlayering function

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 (10)

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 ⋮ Random polarizations ⋮ Convergence properties of symmetrization processes ⋮ DEFORMING A CONVEX DOMAIN INTO A DISK BY KLAIN’S CYCLIC REARRANGEMENT ⋮ On some determinant and matrix inequalities with a geometrical flavour ⋮ Ergodic properties of folding maps on spheres ⋮ Symmetrization in geometry

Cites Work

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• A countable set of directions is sufficient for Steiner symmetrization
• 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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