Degenerate Complex Monge-Ampere Equations on Some Compact Hermitian Manifolds

Let X be a compact complex manifold which admits a hermitian metric satisfying a curvature condition introduced by Guan-Li. Given a semipositive form theta with positive volume, we define the Monge-Amp & egrave;re operator for unbounded theta-psh functions and prove that it is continuous with respect to convergence in capacity. We then develop pluripotential tools to study degenerate complex Monge-Ampere equations in this context, extending recent results of Tosatti-Weinkove, Kolodziej-Nguyen, Guedj-Lu and many others who treat bounded solutions.