  We conjecture that for every dimension n not equal 3 there exists a
noncompact hyperbolic n-manifold whose volume is smaller than the volume of any
compact hyperbolic n-manifold. For dimensions n at most 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 at
least 30.
