Systoles and kissing numbers of finite area hyperbolic surfaces
  We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main result is a bound which only depends on the topology of the surface and which grows subquadratically in the genus. 
Federica Fanoni and Hugo Parlier
math.GT math.DG