Abstract
In this paper 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, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure.
Citation
Arseniy Akopyan. Alfredo Hubard. Roman Karasev. "Lower and upper bounds for the waists of different spaces." Topol. Methods Nonlinear Anal. 53 (2) 457 - 490, 2019. https://doi.org/10.12775/TMNA.2019.008