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The minimal volume of orientable hyperbolic manifolds with a given number ofcusps has been found for $0,1,2,4$ cusps, while the minimal volume of 3-cuspedorientable hyperbolic manifolds remains unknown. By using guts in suturedmanifolds and pared manifolds, we are able to show that for an orientablehyperbolic 3-manifold with 3 cusps such that every second homology class islibroid, its volume is at least $5.49\ldots = 6 \times $Catalan's constant.

Guts and The Minimal Volume Orientable Hyperbolic 3-Manifold with 3 Cusps