On the Steiner inequality for the \(L_p\) surface area
type: Item
instance of: scholarly article
title: On the Steiner inequality for the \(L_p\) surface area
author: Zixin Cao
author: Tuo Wang
author: Yanhui Wang
published in: Advances in Mathematics
publication date: 2024-11-18T00:00:00Z
review text: The authors consider Steiner inequalities for the \(L_p\) surface area for \(p > 1\). They give two approaches: One bases on the machinery of \textit{E. Lutwak} et al. [Int. Math. Res. Not. 2006, No. 1, Article ID 62987, 21 p. (2006; Zbl 1110.46023)].\N\NThe other is a direct proof of the Steiner inequality for the \(L_p\) surface area. Also, the authors provide a new proof of Lutwak's \(L_p\) isoperimetric inequalities for \(p > 1\) together with equality conditions.
reviewed by: S. S. Kutateladze
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A38
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 7945729
zbMATH Keywords: functional \(L_p\) Minkowski problems
zbMATH Keywords: Steiner inequalities
zbMATH Keywords: isoperimetric inequality
zbMATH Keywords: \(L_p\) Brunn-Minkowski theory
zbMATH Keywords: \(L_p\) surface area
zbMATH Keywords: Pólya-Szegö principle
MaRDI profile type: Publication
cites work: Convex symmetrization and applications
cites work: Problèmes isoperimetriques et espaces de Sobolev
cites work: Stronger versions of the Orlicz-Petty projection inequality
cites work: Weighted Dirichlet-type inequalities for Steiner symmetrization
cites work: Q3771040
cites work: Steiner symmetrization is continuous in \(W^{1,p}\)
cites work: The \(L^p\)-Busemann-Petty centroid inequality
cites work: The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
cites work: A quantitative Pólya-Szegö principle
cites work: Steiner symmetric extremals in Pólya-Szegő-type inequalities
cites work: Affine Moser-Trudinger and Morrey-Sobolev inequalities
cites work: A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
cites work: Q3707973
cites work: Completion for Steiner`s basic geometric proofs of the Theorem that a circle possesses a greater area than each other plane figure with same circuit.
cites work: Quantitative Pólya-Szegö principle for convex symmetrization
cites work: Convex symmetrization and Pólya--Szegö inequality.
cites work: Minimal rearrangements of Sobolev functions: A new proof.
cites work: Convex rearrangement: Equality cases in the Pólya-Szegö inequality
cites work: $p$-Means of Convex Bodies.
cites work: Zur Geschichte des isoperimetrischen Problems
cites work: Convex and Discrete Geometry
cites work: General \(L_{p}\) affine isoperimetric inequalities
cites work: An asymmetric affine Pólya-Szegő principle
cites work: On the \(L_{p}\) Minkowski problem for polytopes
cites work: Analysis.
cites work: Ellipsoids and matrix-valued valuations
cites work: Minkowski valuations
cites work: Valuations on Sobolev spaces
cites work: \(\mathrm{SL}(n)\) invariant valuations on polytopes
cites work: On some affine isoperimetric inequalities
cites work: The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
cites work: The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
cites work: On the regularity of solutions to a generalization of the Minkowski problem
cites work: \(L_ p\) affine isoperimetric inequalities.
cites work: A new ellipsoid associated with convex bodies
cites work: Sharp affine \(L_ p\) Sobolev inequalities.
cites work: On the $L_{p}$-Minkowski problem
cites work: Optimal Sobolev norms and the Lp Minkowski problem
cites work: The Brunn-Minkowski-Firey inequality for nonconvex sets
cites work: Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory
cites work: Q3995421
cites work: Q5287551
cites work: Beweis des Satzes, dass die Kugel kleinere Oberfläche besitzt, als jeder andere Körper gleichen Volumens.
cites work: Best constant in Sobolev inequality
cites work: The affine Sobolev-Zhang inequality on BV(\(\mathbb R^n)\)
cites work: The affine Pólya-Szegö principle: equality cases and stability
cites work: Semi-Valuations on $BV(\\mathbb R^n)$
cites work: On the Discrete FunctionalLpMinkowski Problem
cites work: A new capacity for the affine bounded variation
cites work: The affine Sobolev inequality.
DOI: 10.1016/J.AIM.2024.109997
description: scientific article; zbMATH DE number 7945729