1. CMB 2013 (vol 57 pp. 870)
||A Short Note on Short Pants|
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 SeppÃ¤lÃ¤. The goal of this note is to give a short proof of a linear upper bound which slightly improve the best known bound.
Keywords:hyperbolic surfaces, geodesics, pants decompositions
Categories:30F10, 32G15, 53C22
2. CMB 2002 (vol 45 pp. 89)
||On Gunning's Prime Form in Genus $2$ |
Using a classical generalization of Jacobi's derivative formula, we
give an explicit expression for Gunning's prime form in genus 2 in
terms of theta functions and their derivatives.