The complex Hessian quotient flow on compact Hermitian manifolds

In this paper, we consider the parabolic Hessian quotient equation on compact Hermitian manifolds. By setting up a priori estimates of the admissible solutions, we prove the long-time existence of the solution to the parabolic Hessian quotient equation and its convergence. As an application, we show the solvability of a class of complex Hessian quotient equations, which generalizes the relevant results.