Isospectral finiteness on convex cocompact hyperbolic 3-manifolds
  In this paper we show that a given set of lengths of closed geodesics, there are only finitely many convex cocompact hyperbolic 3-manifolds with that specified length spectrum, homotopy equivalent to a given 3-manifold without a handlebody factor, up to orientation preserving isometries. 
Gilles Courtois and Inkang Kim
math.GT