3 problems

Buser's conjecture. The surface $M$ has a pants decomposition in which each curve has length at most

Let $K$ be a surface of genus $g$ embedded in ${\mathbb{R}}^N$ by a bilipschitz map, and let $\gamma_1,\dots,\gamma_{3g-3}$ be the boundary curves of a pants decomposition of $K$.…

Let $g$ and $n$ denote the genus and number of cusps of a hyperbolic surface, respectively. Its Bers' constant is the smallest number such that the surface admits a pants decomposi…