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In this paper, we consider fully nonlinear equations of Krylov type onRiemannian manifolds with negative curvature which naturally arise in conformalgeometry. Moreover, we prove the a priori estimates for solutions to theseequations and establish the existence results. Our results can be viewed as anextension of previous results given by Gursky-Viaclovsky and Li-Sheng.

Fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature