Smoothness of the Steiner symmetrization

DOI10.1090/proc/13683zbMath1410.52002OpenAlexW2591448440MaRDI QIDQ4590989

Youjiang Lin

Publication date: 21 November 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13683

zbMATH Keywords

Gauss curvatureorthogonal projectionSteiner symmetrization\(C^2\) convex body

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (7)

The equality cases in Steiner's projection inequality ⋮ Lipschitz star bodies ⋮ The Petty projection inequality for sets of finite perimeter ⋮ \(k\)-codimensional projection bodies ⋮ The affine Orlicz Pólya-Szegő principle on \(BV(\Omega )\) ⋮ Minkowski symmetrization and projection bodies ⋮ Affine Pólya-Szegő inequality on Steiner rearrangement in any codimension

Cites Work

• Stronger versions of the Orlicz-Petty projection inequality
• A countable set of directions is sufficient for Steiner symmetrization
• Symmetrization in geometry
• Orlicz centroid bodies
• Orlicz projection bodies
• Symmetrals and X-rays of planar convex bodies
• Steiner symmetrization is continuous in \(W^{1,p}\)
• Steiner symmetrals and their distance from a ball
• \(L_ p\) affine isoperimetric inequalities.
• A Helmholtz-Lie type characterization of ellipsoids. II
• How Smooth is the Shadow of a Smooth Convex Body?
• The Brunn-Minkowski inequality
• Convex and Discrete Geometry
• Convex Bodies The Brunn-MinkowskiTheory
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