Notes on the peripheral volume of hyperbolic 3‐manifolds

We consider orientable hyperbolic 3‐manifolds with either non‐empty compact geodesic boundary, or some toric cusps, or both. For any such M we analyze what portion of the volume of M can be recovered by inserting in M boundary collars and cusp neighbourhoods with disjoint embedded interiors. Our main result is that this portion can only be maximal in some combinatorially extremal configurations. The techniques we employ are very elementary but the result is in our opinion of some interest.