Systole growth for finite area hyperbolic surfaces
  We are interested in the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g,n)$. This maximum is shown to be strictly increasing in terms of the number of cusps for small values of $n$. We also show that this function is greater than a function that grows logarithmically in function of the ratio $g/n$. 
Florent Balacheff and Eran Makover and Hugo Parlier
math.GT math.DG