Fully non-linear elliptic equations on noncompact complex manifolds

In this paper, we establish a priori estimates and existence results for solutions of a general class of fully non-linear equations on noncompact Kähler and Hermitian manifolds. As geometric applications, we construct complete Kähler metrics with prescribed volume forms on strictly pseudoconvex domains, as well as find Einstein metrics on complete noncompact Kähler manifolds and Hessian manifolds with negative first Chern class.