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

Abstract

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].

arXiv comment36 pages

References in corpus (1)

• On Gromov's Waist of the Sphere Theorem

Cited by in corpus (1)

• Convex Equipartitions of volume and surface area