Hyperbolic manifolds of small volume (Q462614)

Summary: We conjecture that for every dimension \(n \neq 3\) there exists a noncompact hyperbolic \(n\)-manifold whose volume is smaller than the volume of any compact hyperbolic \(n\)-manifold. For dimensions \(n \leq 4\) and \(n = 6\) this conjecture follows from the known results. In this paper we show that the conjecture is true for arithmetic hyperbolic \(n\)-manifolds of dimension \(n\geq 30\).