It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in genus, a theorem of Buser and Seppälä. The goal of this note is to give a short proof of a linear upper bound which slightly improve the best known bound.
hyperbolic surfaces, geodesics, pants decompositions
30F10 - Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
32G15 - Moduli of Riemann surfaces, Teichmuller theory [See also 14H15, 30Fxx]
53C22 - Geodesics [See also 58E10]