发表机构
University of Western Macedonia; Aristotle University of Thessaloniki（西马其顿大学; 塞萨洛尼基亚里士多德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过证明平面 John 域共形等价于圆域，证明了 Koebe 猜想，并利用跨界模量给出充要条件。
AI 中文摘要
我们通过证明每个平面 John 域共形等价于一个圆域，证明了 John 域的 Koebe 猜想。我们的证明基于 John 域的一个几何性质，并证明该性质足以通过圆域进行均匀化。作为推论，我们获得了内均匀域和 Gromov 双曲域的 Koebe 猜想的另一种证明，恢复了作者早期工作中建立的结果。最后，我们利用 Schramm 的跨界模量以及第二作者与 Rajala 构造的圆域的良性穷竭，推导出域满足 Koebe 猜想的充要条件。
英文摘要
We prove Koebe's conjecture for John domains by showing that every planar John domain is conformally equivalent to a circle domain. Our proof is based on a geometric property of John domains, which we prove to be sufficient for uniformization by a circle domain. As a consequence, we obtain an alternative proof of Koebe's conjecture for inner uniform and Gromov hyperbolic domains, recovering results established in earlier work of the authors. Finally, we derive a necessary and sufficient condition for a domain to satisfy Koebe's conjecture by using Schramm's transboundary modulus and well-behaved exhaustions of circle domains constructed by the second author and Rajala.
Comments27 pages, 5 figures
