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

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

2010-01-01

arxiv.org/abs/1001.0260v1

Mathematics

Metric Geometry

36 pages

Scientific paper

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].

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