On extremal Riemann surfaces and their uniformizing fuchsian groups
On extremal Riemann surfaces and their uniformizing fuchsian groups
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极值黎曼曲面及其均匀化 fuchsian 群
DOI：
10.1017/s0017089502010108
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发表时间：
2002
影响因子：
0.5
通讯作者：
G. González‐diez
中科院分区：
文献类型：
--
作者：
E. Girondo;G. González‐diez
已经从不同的角度研究了包含最大半径圆盘的给定属 g 的紧双曲曲面。在本文中，我们将这些不同的方法联系起来，并观察均匀化致密极值表面和刺穿极值表面的 Fuchsian 群的一些属性。我们还表明，属 g=2,3 的极值面可能包含一个或多个极值盘，而极值盘对于 g \ge 4 来说必然是唯一的。在此过程中，我们还构造了显式的极值面族，其中之一被证明是不存在自同构的。
Compact hyperbolic surfaces of given genus g containing discs of the maximum radius have been studied from various points of view. In this paper we connect these different approaches and observe some properties of the Fuchsian groups uniformizing both compact and punctured extremal surfaces. We also show that extremal surfaces of genera g=2,3 may contain one or several extremal discs, while an extremal disc is necessarily unique for g \ge 4. Along the way we also construct explicit families of extremal surfaces, one of which turns out to be free of automorphisms.