On iterations of Steiner symmetrizations

DOI10.1007/S10231-015-0539-2zbMath1360.60035OpenAlexW2231736279MaRDI QIDQ325954

Aljoša Volčič

Publication date: 11 October 2016

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-015-0539-2

zbMATH Keywords

isoperimetric problemCaccioppoli setsSteiner symmetrization

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Inequalities and extremum problems involving convexity in convex geometry (52A40)

Related Items (5)

Generalization of Klain’s theorem to Minkowski symmetrization of compact sets and related topics ⋮ Convergence of symmetrization processes ⋮ Lipschitz star bodies ⋮ Convergence properties of symmetrization processes ⋮ The Petty projection inequality for sets of finite perimeter

Cites Work

• Steiner symmetrization using a finite set of directions
• 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
• Steiner symmetrization is continuous in \(W^{1,p}\)
• Random polarizations
• Random Steiner symmetrizations of sets and functions
• A weighted isoperimetric inequality and applications to symmetrization
• Su una teoria generale della misura \((r-1)\)-dimensionale in uno spazio ad \(r\) dimensioni
• Convergence in shape of Steiner symmetrizations
• Random Symmetrizations of Convex Bodies
• A partial solution of the isoperimetric problem for the Heisenberg group
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