The Dirichlet Problem for a Complex Monge-Ampere Type Equation on Hermitian Manifolds

Abstract

We are concerned with fully nonlinear elliptic equations on complex manifolds and search for technical tools to overcome difficulties in deriving a priori estimates which arise due to the nontrivial torsion and curvature, as well as the general (non-pseudoconvex) shape of the boundary. We present our methods, which work for more general equations, by considering a specific equation which resembles the complex Monge-Ampere 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.

Revised version based on the referees' reports, we would like to thank them for their helpful comments

References in corpus (2)

• On the evolution of a Hermitian metric by its Chern-Ricci form
• Taming symplectic forms and the Calabi-Yau equation

Cited by in corpus (1)

• On a class of fully nonlinear elliptic equations on Hermitian manifolds