# Waist of balls in hyperbolic and spherical spaces

## TL;DR

This paper provides precise estimates for the Gromov waist of balls in spaces of constant curvature, extending results to Riemannian manifolds with curvature bounds and normed spaces, advancing geometric measure theory.

## Contribution

It introduces tight bounds for Gromov's waist in various geometric spaces, including hyperbolic, spherical, and normed spaces, generalizing previous results.

## Key findings

- Tight estimates for Gromov's waist in constant curvature spaces
- Extension of waist estimates to $ ext{CAT}(\kappa)$-spaces
- Results applicable to normed spaces

## Abstract

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 ($\mathrm{CAT}(\kappa)$-spaces), and establish similar result for normed spaces.