The Dirichlet problem for degenerate complex Monge-Ampere equations
Differential Geometry
2009-04-14 v1 Complex Variables
Abstract
The Dirichlet problem for a Monge-Ampere equation corresponding to a nonnegative, possible degenerate cohomology class on a Kaehler manifold with boundary is studied. C^{1,\alpha} estimates away from a divisor are obtained, by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory. In particular, C^{1,\alpha} geodesic rays in the space of Kaehler potentials are constructed for each test configuration
Cite
@article{arxiv.0904.1898,
title = {The Dirichlet problem for degenerate complex Monge-Ampere equations},
author = {D. H. Phong and Jacob Sturm},
journal= {arXiv preprint arXiv:0904.1898},
year = {2009}
}