  In this paper we examine the geometry of minimal surfaces of arithmetic
hyperbolic 3-manifolds. In particular, we give bounds on the totally geodesic
2-systole, construct infinitely many incommensurable manifolds with the same
initial geometric genus spectrum in which volume and 1-systole are controlled,
and analyze the growth of the genera of minimal surfaces across
commensurability classes. These results have applications to the study of how
Heegard genus grows across commensurability classes.
