Results 101 to 110 of about 120,054 (119)

On iterations of Steiner symmetrizations

Annali di Matematica Pura ed Applicata (1923 -), 2015
Let \(N\) be a positive integer and let \(u \in \mathbb{S}^{N-1} := \{ x \in \mathbb{R}^N : \| x \| = 1 \}\) denote the unit sphere. The \textit{Steiner symmetrization} in the direction \(u\) is a mapping \(S_u\) of measurable subsets of \(\mathbb{R}^N\) to measurable subsets of \(\mathbb{R}^N\), acting as follows.
openaire   +1 more source

Symmetric abelian group-invariant Steiner quadruple systems

Journal of Combinatorial Theory, Series A, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lijun Ji, Xiao-Nan Lu
openaire   +2 more sources

Quantitative Steiner/Schwarz-type symmetrizations

Geometriae Dedicata, 1996
Considering higher dimensional symmetrizations the author shows that very few of them suffice to bring a symmetric convex body close to a Euclidean ball. Further, the author proves that very few Schwarz symmetrizations suffice to bring a body to a distance at most \(1 + \varepsilon\) for every given \(\varepsilon\).
openaire   +1 more source

Stability for the Dirichlet Problem under Continuous Steiner Symmetrization

Potential Analysis, 2000
The authors present a nice construction that deforms an arbitrary open set into a ball. During the transformation the measure of the set stays invariant, the first Dirichlet-Laplace eigenvalue keeps decreasing, and the \(k\)-th eigenvalue is continuous from the left.
Bucur, Dorin, Henrot, Antoine
openaire   +1 more source

Random Steiner symmetrizations of sets and functions

Calculus of Variations and Partial Differential Equations, 2012
Let \(\mathcal{L}^N\) be the \(N\)-dimensional Lebesgue measure and \(\mathcal{M}\) be the family of all measurable sets of the \(N\)-dimensional Euclidean space \({\mathbb R}^N\) having finite measure. Denote by \(B(x, \rho)\) the closed ball centered at \(x\) having radius \(\rho\). The unit sphere of \({\mathbb R}^N\), that is the set of all vectors
openaire   +1 more source

Planar Poincaré domains: Geometry and Steiner symmetrization

Journal d'Analyse Mathématique, 1995
A planar domain \(\Omega\) is called a \(b\)-strip if each cross-section \( \Omega_x = \{y : (x,y) \in \Omega\}\) is either empty or an interval of length no greater than \(b\). The authors provide necessary and sufficient conditions on strip domains \(\Omega\) in order for them to be \(p\)-Poincaré domains, i.e.
Smith, Wayne, Stanoyevitch, Alexander, Stegenga, David A.   +2 more
openaire   +2 more sources

Isomorphic Steiner symmetrization of $$p$$ p -convex sets

Geometriae Dedicata, 2013
Denote by \(D_n\) the \(n\)-dimensional Euclidean unit ball and by \(\kappa_n\) its Lebesgue measure. According to \textit{B. Klartag} and \textit{V. D. Milman} [Invent. Math. 153, No. 3, 463--485 (2003; Zbl 1034.52008)], there exist universal positive constants \(c\) and \(C\) such that for each convex body \(K \subset \mathbb R^n\) with \(|K ...
openaire   +1 more source

Steiner symmetrization and applications

2005
Proceedings of "The Renato Caccioppoli Centenary Conference", Napoli ...
openaire   +1 more source

A Result on the Steiner Symmetrization of a Compact Set

Journal of the London Mathematical Society, 1976
openaire   +2 more sources

Steiner symmetrization $$(n-1)$$ times is sufficient to transform an ellipsoid to a ball in $${\mathbb {R}}^n$$

Annales Mathematiques Du Quebec, 2020
Ge Xiong
exaly