On Gromov's Waist of the Sphere Theorem

The goal of this paper is to give a detailed and complete proof of M. Gromov's waist of the sphere theorem.Comment: 34 pages, 1 figur

A Lower Bound on the Waist of Unit Spheres of Uniformly Convex Normed Spaces

In this paper we give a lower bound on the waist of the unit sphere of a uniformly convex normed space by using the localization technique in codimension greater than one and a strong version of the Borsuk-Ulam theorem. The tools used in this paper follow ideas of M. Gromov in [4]. Our isoperimetric type inequality generalizes the Gromov-Milman isoperimetric inequality in [5].Comment: 36 page

Géométrie de l'espace des cycles : waist et graphes minimaux

The thesis presented here consists of three papers, entitled "On Gromov's Waist of the Sphere Theorem", "A Lower Bound on the Waist of Unit Spheres of Uniformly Convex Normed Spaces" and "On the Maximum Number of Vertices of Minimal Embedded Graphs". These topics are connected and form part of the same problem, which belongs to the geometry of cycle spaces.La thèse qui est présentée ici est composée de trois articles, intitulés "On Gromov’s Waist of the Sphere Theorem", "A Lower Bound on the Waist of Unit Spheres of Uniformly Convex Normed Spaces" et "On the Maximum Number of Vertices of Minimal Embedded Graphs". Ces sujets se relient et font partie d’un même problème qui appartient à la géométrie des espaces des cycles