标题： 无限亏格的手柄体和施托基群 显示英文标题

标题： Handlebodies of Infinite Genus and Schottky Groups

摘要： 在本文中，我们通过为它们提供适当的定义，开始对无限亏格的流体、无限生成的施托克群以及相关的统一问题进行研究。 具有非平面端点的无限亏格曲面有不可数多个拓扑类型。 我们证明，任何这样的曲面和任何无限亏格的流体都可以通过一个无限生成的经典施托克群进行拓扑统一。 接下来，我们证明了一个具有非平面端点并接受有界裤分解的无限亏格黎曼曲面可以通过一个经典施托克群进行拟共形统一。 此外，这种统一的共形等价类是唯一的。如果去掉有界裤分解的假设，我们提供了一些这样的黎曼曲面的例子，它们不接受通过施托克群的拟共形统一。 显示英文摘要

摘要： In this paper, we begin an investigation of infinite genus handlebodies, infinitely generated Schottky groups, and related uniformization questions by giving appropriate definitions for them. There are uncountably many topological types of infinite genus surfaces with non-planar ends. We show that any such surface and any infinite genus handlebody can be topologically uniformized by an infinitely generated classical Schottky group. We next show that an infinite genus Riemann surface with non-planar ends admitting a bounded pants decomposition can be quasiconformally uniformized by a classical Schottky group. In addition, the conformal equivalence class of such a uniformization is unique.If the assumption of bounded pants decomposition is removed we supply examples of such Riemann surfaces that do not admit a quasiconformal uniformization by a Schottky group.