  The Heegaard genus of a 3-manifold, as well as the growth of Heegaard genus
in its finite sheeted cover spaces, has extensively been studied in terms of
algebraic, geometric and topological properties of the 3-manifold. This note
shows that analogous results concerning the trisection genus of a smooth,
orientable 4-manifold have more general answers than their counterparts for
3-manifolds. In the case of hyperbolic 4-manifolds, upper and lower bounds are
given in terms of volume and a trisection of the Davis manifold is described.
