Volumes of balls in Riemannian manifolds and Uryson width [article]

Larry Guth
2015 arXiv   pre-print
If (M^n, g) is a closed Riemannian manifold where every unit ball has volume at most ϵ_n (a sufficiently small constant), then the (n-1)-dimensional Uryson width of (M^n, g) is at most 1.
arXiv:1504.07886v1 fatcat:afgw5ngosbddlh4cyeqo5tubza