Adapted renormalized volume for hyperbolic 3-manifolds with compressible boundary

Given a hyperbolizable 3-manifold N, the renormalized volume is a real-analytic function on the space of convex co-compact hyperbolic structures on the interior of N, which always have infinite hyperbolic volume. When the boundary of N is incompressible the renormalized volume is always non-negative, otherwise it has infimum −∞. After introducing the renormalized volume, and its behavior in the case of N having compressible boundary, we present a new adapted version for this setting.

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