Hessian Equations of Krylov Type on Kähler Manifolds

In this paper, we consider Hessian equations with its structure as a combination of elementary symmetric functions on closed Kähler manifolds. We provide a sufficient and necessary condition for the solvability of these equations, which generalize the results of Hessian equations and Hessian quotient equations. As a consequence, we solve a complex Monge-Ampère type equation which was proposed by Chen.

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