Renormalized volume and the volume of the convex core

TL;DR

This paper establishes bounds relating the renormalized volume and the convex core volume in convex cocompact hyperbolic 3-manifolds, extending previous results to more general settings.

Contribution

It provides new bounds connecting renormalized volume and convex core volume based on boundary injectivity radius and Euler characteristic, generalizing prior work.

Findings

Derived upper and lower bounds for volume differences

Extended Schlenker's results to broader classes of hyperbolic 3-manifolds

Connected geometric invariants with topological and boundary properties

Abstract

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.