Lower and upper bounds for the waists of different spaces

Arseniy Akopyan, Alfredo Hubard, Roman Karasev


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.


Waist inequality; isoperimetric inequality

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