Uryson width and volume

We give a short proof of a theorem of Guth relating volume of balls and Uryson width. The same approach applies to Hausdorff content implying a recent result of Liokumovich–Lishak–Nabutovsky–Rotman. We show also that for any C>0 there is a Riemannian metric g on a 3-sphere such that vol(S3,g)=1 a...