The Dirichlet problem for Monge-Ampère type equations on Riemannian manifolds

In this paper, we study the Dirichlet problem for Monge-Ampère type equations for $p$-plurisubharmonic functions on Riemannian manifolds. The $a$ $priori$ estimates up to the second order derivatives of solutions are established. The existence of a solution then follows by the continuity method.