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. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Notes on the peripheral volume of hyperbolic 3-manifolds / Petronio, C.; Tocchet, M.. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 287:5-6(2014), pp. 677-685. [10.1002/mana.201200180]
Notes on the peripheral volume of hyperbolic 3-manifolds
Petronio C.;
2014-01-01
Abstract
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. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
