Lower and upper bounds for the waists of different spaces
Differential Geometry
2019-12-30 v2 Metric Geometry
Abstract
We prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk--Ulam--Crofton technique. We consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space. We establish waist-type results in terms of the Hausdorff measure.
Keywords
Cite
@article{arxiv.1612.06926,
title = {Lower and upper bounds for the waists of different spaces},
author = {Arseniy Akopyan and Alfredo Hubard and Roman Karasev},
journal= {arXiv preprint arXiv:1612.06926},
year = {2019}
}