Renormalization-group equations in curved space-time

Renormalization-group equations are given a general formulation in curved space-time. The general form of the equation for the effective charge corresponding to the parameter of nonminimal coupling of a scalar field and the gravitational field is established in the one-loop approximation. It is shown that in the limit of a strong gravitational field the asymptotically free theories can be asymptotically conformally invariant.