Uryson width and pants decompositions of hyperbolic surfaces

Abstract

Suppose that $M$ is a hyperbolic surface of genus $g$ and with $n$ cusps. Then we can find a pants decomposition of $M$ composed of simple closed geodesics so that each curve is contained in a ball of diameter at most $C\sqrt{g+n}$, where $C$ is a universal constant.

arXiv comment12 pages