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