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arXiv · 1712.00405

The Dirichlet Problem for the Complex Homogeneous Monge-Amp\`ere Equation

Julius Ross·David Witt Nyström
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Abstract

We survey the Dirichlet problem for the complex Homogeneous Monge-Amp\`ere Equation, both in the case of domains in $\mathbb C^n$ 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.

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Julius Ross, David Witt Nyström. 2017-12-01. The Dirichlet Problem for the Complex Homogeneous Monge-Amp\`ere Equation. https://arxiv.org/abs/1712.00405

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