Waist of balls in hyperbolic and spherical spaces

In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature ($\mathrm{C}\mathrm{A}\mathrm{T}(\kappa )$-spaces), and establish similar result for normed spaces.