【作者】 沈亚良；

【导师】 沈玉良；

【作者基本信息】 苏州大学 ， 基础数学， 2002， 硕士

【摘要】 本文第一部分以Schwarz-Christoffel变换为基础，对边序列为baabaa的等角六边形H的单叶性内径进行了讨论。L.Wieren证明了当1≤b/a≤1.67117…时，H是一个Nehari圆，并且σ（H）=8／9=σ（P₆）。运用L.Wieren的方法，并综合使用数学软件包Mathematica和Maple，我们证明了当0.6157…≤b/a≤1时，H仍然是一个Nehari圆，并且σ（H）=8／9=σ（P₆）。 本文的第二部分把双曲Riemann曲面上关于极值拟共形映射的一些结果进行了推广。在曲面R=UR_i上，其中每个R_i是一个双曲Riemann曲面，R_i∩R_j=φ，i≠j，I是非空指标集，我们类似地给出了极值，唯一极值，无穷小极值，唯一无穷小极值等概念，并把双曲Riemann曲面上极值Beltrami微分的Hamilton-Krushkal条件推广到该曲面上。我们还讨论了平面上闭子集的Teichmüllter空间中的极值问题，并得到了一些类似的结果。更多还原

【Abstract】 In the first part of this article, we discuss the problem on the inner radius of uni-valency for an equiangular hexagon H whose sides form the sequence baabaa. L.Wieren proved that if 1 < b/a < 1.67117..., then H is a Nehari disk and a(H) = 8/9 = (P6). Using the methods developed by L.Wieren, we prove that H is still a Nehari disk and a(H) = 8/9 = (-Pe) when 0.6157... < b/a < 1. In the proof, we use the Mathematica software package and the Maple software package.In the second part of this article, we extend some results on extremal quasiconfor-mal mappings between hyperbolic Riemann surfaces. On the surface R = Ri, whereevery Ri is a hyperbolic Riemann surface, Ri Rj = , i j, and / is a non-empty index set, we introduce the concepts of extremality, unique extremality, infinitesimal extremality and unique infinitesimal extremality, and extend the Hamilton-Krushkal condition for extremal Beltrami differentials of the hyperbolic Riemann surface to this case. We also discuss the extremal problem for Teichmuller spaces of closed subsets of the sphere and obtain some similar results.更多还原