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Spherical Steiner Symmetrizations

Axioms
In this paper, we primarily investigate and establish several properties of spherical Steiner symmetrizations, along with the isoperimetric property of the spherical cap in Sn.
Youjiang Lin, Zhilang Deng
doaj   +2 more sources

Isomorphic Steiner symmetrization [PDF]

Inventiones Mathematicae, 2003
Throughout the last 160 years, Steiner symmetrization has become a major tool for proving various geometric inequalities. It is clear that consecutive Steiner symmetrizations make the body closer to a Euclidean ball. Since many years ago mathematicians have been interested in estimating how many symmetrizations are necessary for that convergence.
Klartag, B., Milman, V. D.
exaly   +2 more sources

Steiner symmetrization: a weighted version of Pólya-Szegö principle [PDF]

Nonlinear Differential Equations and Applications, 2007
n ...
Luca Esposito, Cristina Trombetti, Trombetti Cristina   +2 more
exaly   +5 more sources

A new Steiner symmetrization defined by a subclass of analytic function in a complex domain

Frontiers in Applied Mathematics and Statistics
In this effort, we present a new definition of the Steiner symmetrization by using special analytic functions in a complex domain (the open unit disk) with respect to the origin.
Rabha W Ibrahim, Alazman Ibtehal, Ibrahim Rabha W   +2 more
exaly   +3 more sources

The perimeter inequality under Steiner symmetrization: Cases of equality [PDF]

Annals of Mathematics, 2005
Steiner symmetrization is known not to increase perimeter of sets in Rn. The sets whose perimeter is preserved under this symmetrization are characterized in the present paper.
Miroslav Chlebík, Andrea Cianchi, Nicola Fusco   +2 more
exaly   +4 more sources

Symmetrization theorem of full steiner trees

Journal of Combinatorial Theory - Series A, 1994
The paper contributes to the plane Steiner problem by a symmetrization theorem. The topology of a full Steiner tree with an even number of regular points (and of Steiner points) is called symmetric iff there is a fixpoint-free 1-1 correspondence of all points preserving adjacency and preserving the circular ordering of the neighbors of each Steiner ...
exaly   +2 more sources

A countable set of directions is sufficient for Steiner symmetrization

Advances in Applied Mathematics, 2011
6 ...
Gabriele Bianchi, Daniel A Klain, Erwin Lutwak   +2 more
exaly   +3 more sources

Symmetry theorems via the continuous steiner symmetrization

Electronic Journal of Differential Equations, 2000
Using a new approach due to F. Brock called the Steiner symmetrization, we show first that if $u$ is a solution of an overdetermined problem in the divergence form satisfying the Neumann and non-constant Dirichlet boundary conditions, then $Omega$ is an ...
L. Ragoub
doaj   +2 more sources

A Steiner Inequality for the Anisotropic Perimeter

Journal of Function Spaces, 2022
In this paper, we prove the monotonicity of the anisotropic perimeter of sets of finite perimeter under Steiner symmetrization by a variational formula of volume and an inequality for the anisotropic lower outer Minkowski content.
Jin Dai
doaj   +1 more source

On Isoperimetric Inequalities in Minkowski Spaces

Journal of Inequalities and Applications, 2010
The purpose of this expository paper is to collect some (mainly recent) inequalities, conjectures, and open questions closely related to isoperimetric problems in real, finite-dimensional Banach spaces (= Minkowski spaces).
Horst Martini, Zokhrab Mustafaev
doaj   +2 more sources