Systole growth for finite area hyperbolic surfaces

Abstract

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 $g/n$.

8 pages, 1 figure. Removed Part 3 of main theorem due to an error in Lemma 3