Volumes of balls in Riemannian manifolds and Uryson width

Abstract

If $(M^n,g)$ is a closed Riemannian manifold where every unit ball has volume at most ${\epsilon }_n$ (a sufficiently small constant), then the $(n-1)$-dimensional Uryson width of $(M^n,g)$ is at most 1.

arXiv comment26 pages

References in corpus (1)

• Metaphors in systolic geometry