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Displaying 341 –
360 of
2522
We prove some results in the context of isoperimetric inequalities with quantitative terms. In the -dimensional case, our main contribution is a method for determining the optimal coefficients in the inequality , valid for each Borel set with positive and finite area, with and being, respectively, the and the of . In dimensions, besides proving existence and regularity properties of minimizers for a wide class of including the lower semicontinuous extension of , we describe the...
We prove an almost isometric reverse Hölder inequality for the euclidean norm on an isotropic generalized Orlicz ball which interpolates Paouris concentration inequality and variance conjecture. We study in this direction the case of isotropic convex bodies with an unconditional basis and the case of general convex bodies.
On définit une structure de bigèbre différentielle graduée sur la somme directe des complexes cellulaires des permutoèdres, qui contient une sous-bigèbre différentielle graduée dont le complexe sous-jacent est la somme directe des complexes cellulaires des polytopes de Stasheff. Ceci étend des constructions de Malvenuto et Reutenauer et de Loday et Ronco pour les sommets des mêmes polytopes.
A generalization of the theorem of Bajmóczy and Bárány which in turn is a common generalization of Borsuk's and Radon's theorem is presented. A related conjecture is formulated.
A Banach space X is called polyhedral if the unit ball of each one of its finite-dimensional (equivalently: two-dimensional [6]) subspaces is a polytope. Polyhedral spaces were studied by various authors; most of the structural results are due to V. Fonf. We refer the reader to the surveys [1], [2] for other definitions of polyhedrality, main properties and bibliography. In this paper we present a short alternative proof of the basic result on the structure of the unit ball of the polyhedral space...
Given rectangles in a plane whose all sides belong to two perpendicular directions, an algorithm for the construction of the boundary of the union of those rectangles is shown in teh paper.
We consider a class of evolution differential inclusions defining the so-called stop operator arising in elastoplasticity, ferromagnetism, and phase transitions. These differential inclusions depend on a constraint which is represented by a convex set that is called the characteristic set. For (bounded variation) data we compare different notions of solutions and study how the continuity properties of the solution operators are related to the characteristic set. In the finite-dimensional case...
For a finite Coxeter group and a Coxeter element of ; the -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of . Its maximal cones are naturally
indexed by the -sortable elements of . The main result of this paper is that the known bijection cl between -sortable elements and -clusters induces a combinatorial isomorphism of fans. In particular, the -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized
associahedron for . The rays...
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2522