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arXiv · 1612.06926

Lower and upper bounds for the waists of different spaces

Arseniy Akopyan·Alfredo Hubard·Roman Karasev
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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.

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Arseniy Akopyan, Alfredo Hubard, Roman Karasev. 2017-11-06. Lower and upper bounds for the waists of different spaces. https://doi.org/10.12775/tmna.2019.008

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