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A lower bound for the volume of hyperbolic 3-manifolds. (English) Zbl 0694.57005
The author proves a lower bound of 0.00064 for the volume of a complete hyperbolic 3-manifold. This bound has not yet been improved, although in the cusped case much better bounds (and often exact results) are known through the work of the author and C. Adams [see C. Adams, “Noncompact hyperbolic 3-orbifolds of small volume” (preprint 1990); “Limit volumes of hyperbolic 3-orbifolds”, J. Differ. Geom. (to appear); J. Lond. Math. Soc., II. Ser. 38, 555-565 (1988; Zbl 0627.57013); and R. Meyerhoff, Bull. Am. Math. Soc., New Ser. 13, 154-156 (1985; Zbl 0602.57009)].
Reviewer: W.D.Neumann

MSC:
57N10 Topology of general \(3\)-manifolds (MSC2010)
57S30 Discontinuous groups of transformations
51M10 Hyperbolic and elliptic geometries (general) and generalizations
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