Harmonic Discs of Solutions to the Complex Homogeneous Monge-Ampere Equation
Nystrom, David Witt
Publications mathématiques de l'IHÉS
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Ross, J., & Nystrom, D. W. (2015). Harmonic Discs of Solutions to the Complex Homogeneous Monge-Ampere Equation. Publications mathématiques de l'IHÉS, 122 315-335. https://doi.org/10.1007/s10240-015-0074-0
We study regularity properties of solutions to the Dirichlet problem for the complex Homogeneous Monge-Ampere equation. We show that for certain boundary data on P^1 the solution Φ to this Dirichlet problem is connected via a Legendre transform to an associated flow in the complex plane called the Hele-Shaw flow. Using this we determine precisely the harmonic discs associated to Φ. We then give examples for which these discs are not dense in the product, and also prove that this situation persists after small perturbations of the boundary data.
During this work JR was supported by an EPSRC Career Acceleration Fellowship (EP/J002062/1). DWN has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no 329070.
External DOI: https://doi.org/10.1007/s10240-015-0074-0
This record's URL: https://www.repository.cam.ac.uk/handle/1810/254485