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Notes on the peripheral volume of hyperbolic 3‐manifolds
Author(s) -
Petronio Carlo,
Tocchet Michele
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200180
Subject(s) - mathematics , cusp (singularity) , geodesic , boundary (topology) , disjoint sets , volume (thermodynamics) , hyperbolic manifold , pure mathematics , hyperbolic 3 manifold , combinatorics , mathematical analysis , relatively hyperbolic group , geometry , hyperbolic function , physics , quantum mechanics
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.