Prescribing the Ricci curvature of Kähler asymptotically [formula omitted]n manifolds, n > 2

Abstract

An analogue of Calabi's conjecture was posed on a class of complete noncompact Kähler manifolds [5], then solved on the simplest of them, the complex n-space with n > 2 [9]. Here we prove the conjecture in its full generality, by inverting an elliptic complex Monge-Ampère operator between suitable Fréchet spaces of smooth functions vanishing at infinity. A priori estimates benefit from recent simplifications of [2].