Fully non-linear elliptic equations on complex manifolds

In this paper, we study a broad class of fully nonlinear elliptic equations on Hermitian manifolds. On one hand, under the optimal structural assumptions we derive $C^{2,\alpha }$-estimate for solutions of the equations on closed Hermitian manifolds. On the other hand, we treat the Dirichlet problem. In both cases, we prove the existence theorems with unbounded condition.