Hyperbolic manifolds of small volume

Abstract

We conjecture that for every dimension $n\ne 3$ there exists a noncompact hyperbolic $n$-manifold whose volume is smaller than the volume of any compact hyperbolic $n$-manifold. For dimensions $n\le 4$ 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 $n\ge 30$.