复齐次monge - ampantere方程的Dirichlet问题

Proceedings of Symposia in Pure Mathematics Pub Date : 2017-12-01 DOI:10.1090/PSPUM/099/01744

J. Ross, D. Nystrom

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引用次数: 9

摘要

研究了复齐次Monge-Amp ' ere方程的Dirichlet问题，包括$\mathbb C^n$中的定域和由带有边界的Riemann曲面参数化的紧K\ ahler流形。然后，我们给出了一个完整的作者之前的工作，将其与赫勒-肖流联系起来，并给出了几个具体的例子来说明解决这个问题可以显示的各种现象。

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The Dirichlet problem for the complex homogeneous Monge-Ampère equation

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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