The Dirichlet Problem for a Complex Monge-Ampere Type Equation on Hermitian Manifolds
Analysis of PDEs
2013-07-01 v2 Complex Variables
Differential Geometry
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.
Cite
@article{arxiv.1210.5526,
title = {The Dirichlet Problem for a Complex Monge-Ampere Type Equation on Hermitian Manifolds},
author = {Bo Guan and Qun Li},
journal= {arXiv preprint arXiv:1210.5526},
year = {2013}
}
Comments
Revised version based on the referees' reports, we would like to thank them for their helpful comments