arXiv 1209.60962012-09math.CV

可计算Caratheodory理论

Computable Caratheodory Theory

Ilia Binder, Cristobal Rojas, Michael Yampolsky

备注：: arXiv admin note: text overlap with arXiv:1009.3464

摘要：

单位圆盘到单连通区域$W$上的共形Riemann映射是经典复分析的一个中心研究对象。1912年P.Koebe给出的黎曼映射定理的第一个完整证明是构造性的，从那以后，计算黎曼映射的理论方面得到了广泛的研究。Carath odory理论描述了Riemann映射的边界扩张。在本文中，我们开发了其建设性的版本与明确的复杂性界限。

英文摘要：

Conformal Riemann mapping of the unit disk onto a simply-connected domain $W$ is a central object of study in classical Complex Analysis. The first complete proof of the Riemann Mapping Theorem given by P. Koebe in 1912 is constructive, and theoretical aspects of computing the Riemann map have been extensively studied since. Carath{é}odory Theory describes the boundary extension of the Riemann map. In this paper we develop its constructive version with explicit complexity bounds.

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