AI 中文总结
研究极值双曲曲面，基于NEC群一致化引入新方法，得到相关狄利克雷域结构描述，并给出其在极值圆盘配置计数、特定欧拉特征配置确定、隐藏圆盘位置及自同构群描述等方面的应用。
AI 中文摘要
极值双曲曲面是包含最大可能半径嵌入圆盘的有限型双曲曲面。我们基于NEC群的一致化，引入一种针对这些对象的新通用方法，得到了具有尖点和/或测地线边界的曲面与极值圆盘中心相关的狄利克雷域的结构描述。我们还给出了新描述在极值曲面上的一些应用，如极值圆盘配置的有效计数公式、欧拉特征为 -1 和 -2 的每种配置的确定、几个极值曲面族中隐藏极值圆盘的位置以及它们自同构群的完整描述。
英文摘要
Extremal hyperbolic surfaces are finite-type hyperbolic surfaces that contain an embedded disc of the largest possible radius. We introduce a new general approach to these objects, based on the uniformization by NEC groups, obtaining a structural description of the Dirichlet domains associated to extremal disc centers for surfaces with cusps and/or geodesic boundary. We also provide a number of applications of our new description of extremal surfaces, as an effective counting formula for extremal disc configurations, the determination of every such configuration with Euler characteristic -1 and -2, the location of hidden extremal discs in several families of extremal surfaces, and the full description of their automorphism groups.
Comments34 pages, 19 figures
