  In this article we study a class of prescribed curvature problems on complete
noncompact Riemannian manifolds. To be precise, we derive local $C^0$-estimate
under an asymptotic condition which is in effect optimal, and prove the
existence of complete conformal metrics with prescribed curvature functions. A
key ingredient of our strategy is Aviles-McOwen's result or its fully nonlinear
version on the existence of complete conformal metrics with prescribed
curvature functions on manifolds with boundary.
