Notes on the peripheral volume of hyperbolic 3-manifolds

2012/06/07 by Carlo Petronio, Petronio, Carlo, Michele Tocchet +1
Computer Science · Mathematics · #57M50 (Primary) 57M27 (Secondary) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1206.1480

openalex publication_date 2012/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider 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.

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