ALL-ORDER QUANTUM-GRAVITY IN 2 DIMENSIONS

We derive curvature counterterms in two-dimensional gravity coupled to conformal matter up to infinite order. By construction the higher-ord er action is equivalent to a finite first-order theory with an auxilia ry scalar. Due to this equivalence it shares the following remarkable properties: There is no need for gravitational dressing of the cosmolo gical constant, quantization is consistent for any conformal anomaly c of the coupled matter system, and if the coupled matter system is a ( c = d)-dimensional string theory in a euclidean background then the ef fective string theory is (D = d + 2)-dimensional with Minkowski signat ure (1, D - 1). The resulting quantum theory favours flat geometries a nd suppresses both parabolic and hyperbolic singularities.