Lower and upper bounds for the waists of different spaces

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.

References in corpus (3)

• Metaphors in systolic geometry
• A tight estimate for the waist of the ball
• The width-volume inequality

Cited by in corpus (6)

• Mahler's conjecture for some hyperplane sections
• Surface dimension, tiles, and synchronising automata
• Critical central sections of the cube
• Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
• Waist of balls in hyperbolic and spherical spaces
• On the volume of projections of the cross-polytope