The Dirichlet Problem for the Complex Homogeneous Monge-Amp\`ere Equation
Complex Variables
2018-01-25 v2 Differential Geometry
Abstract
We survey the Dirichlet problem for the complex Homogeneous Monge-Amp\`ere Equation, both in the case of domains in and the case of compact K\"ahler manifolds parametrized by a Riemann surface with boundary. We then give a self-contained account of previous work of the authors that connects this with the Hele-Shaw flow, and give several concrete examples illustrating various phenomena that solutions to this problem can display.
Cite
@article{arxiv.1712.00405,
title = {The Dirichlet Problem for the Complex Homogeneous Monge-Amp\`ere Equation},
author = {Julius Ross and David Witt Nyström},
journal= {arXiv preprint arXiv:1712.00405},
year = {2018}
}
Comments
To appear in Proceedings of Symposia in Pure Mathematics. v2 updated metadata only