The Large Distance Limit of the Gravitational Effective Action in   Hyperbolic Backgrounds
  The one-loop effective action for D-dimensional quantum gravity with negative cosmological constant, is investigated in space-times with compact hyperbolic spatial section. The explicit expansion of the effective action as a power series of the curvature on hyperbolic background is derived, making use of heat-kernel and zeta-regularization techniques. It is discussed, at one-loop level, the Coleman-Weinberg type suppression of the cosmological constant, proposed by Taylor and Veneziano. 
A.A. Btsenko, A.D. Odintsov and S. Zerbini