  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.
