Renormalized volume and the volume of the convex core

We obtain upper and lower bounds on the difference between the renormalized volume and the volume of the convex core of a convex cocompact hyperbolic 3-manifold which depend on the injectivity radius of the boundary of the universal cover of the convex core and the Euler characteristic of the boundary of the convex core. These results generalize results of Schlenker obtained in the setting of quasifuchsian hyperbolic 3-manifolds.