The Dirichlet problem for a complex Monge-Ampère type equation on Hermitian manifolds

We are concerned with fully nonlinear elliptic equations on Hermitian manifolds and search for technical tools to overcome difficulties in deriving a priori estimates which arise due to the nontrivial torsion and general (non-pseudoconvex) boundary data. We present our methods, which work for more general equations, by considering a specific equation which resembles the complex Monge-Ampère equation in many ways but with crucial differences. Our work is motivated by recent increasing interests in fully nonlinear equations on complex manifolds from geometric problems.