Abstract

It was shown by Bishop that if Thurston’s K = 2 conjecture holds for some planar domain, then Brennan’s conjecture holds for the Riemann map of that domain as well. In this paper we show numerically that the original counterexample to Thurston’s K = 2 conjecture given by Epstein, Marden and Marković is not a counterexample to Brennan’s conjecture.

中文翻译：

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用 Thurston 的 K = 2 猜想的反例从数值上证实 Brennan 的猜想

摘要

Bishop 证明，如果 Thurston 的K  = 2 猜想适用于某个平面域，那么 Brennan 的猜想也适用于该域的黎曼映射。在本文中，我们用数值证明 了 Epstein、Marden 和 Marković 给出的Thurston K = 2 猜想的原始反例不是 Brennan 猜想的反例。