منابع مشابه
Symmetrization, convexity and applications
Based on permutation enumeration of the symmetric group and ‘generalized’ barycentric coordinates on arbitrary convex polytope, we develop a technique to obtain symmetrization procedures for functions that provide a unified framework to derive new Hermite-Hadamard type inequalities. We also present applications of our results to the Wright-convex functions with special emphasis on their key rol...
متن کاملSymmetrization of Convex Planar Curves
Given a closed convex planar curve, we call great chords the segment connecting two points with parallel tangents. We call great diagonals the support lines of the great chords and mid-parallels the lines through the mid-point of a great chord parallel to the corresponding tangents. Two curves are called parallel if the corresponding great diagonals are parallel. In this paper, we define the pa...
متن کاملSymmetrization and isotropic constants of convex bodies
We investigate the effect of a Steiner type symmetrization on the isotropic constant of a convex body. We reduce the problem of bounding the isotropic constant of an arbitrary convex body, to the problem of bounding the isotropic constant of a finite volume ratio body. We also add two observations concerning the slicing problem. The first is the equivalence of the problem to a reverse Brunn-Min...
متن کاملHarmonic Symmetrization of Convex Sets and of Finsler Structures, with Applications to Hilbert Geometry
David Hilbert discovered in 1895 an important metric that is canonically associated to an arbitrary convex domain Ω in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof of this fact assumes a certain degree of smoothness of the boundary of Ω, and refers to a theorem by Busemann and Mayer that produces the norm of a tangent vector from the distance f...
متن کاملStability of the Steiner symmetrization of convex sets
The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 1997
ISSN: 0294-1449
DOI: 10.1016/s0294-1449(97)80147-3