The Dirichlet Problem for the Complex Homogeneous Monge-Ampère Equation

2017/12/01 by Ross, Julius, Nyström, David Witt · 1 citation
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.00405

Abstract

We survey the Dirichlet problem for the complex Homogeneous Monge-Ampère Equation, both in the case of domains in \mathbb Cⁿ and the case of compact Kähler 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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