圆的Möbius变换构成极大收敛群
Möbius Transformations of the Circle Form a Maximal Convergence Group
摘要：
研究了拟对称群与收敛群作用在圆上的关系。我们证明了圆的莫比乌斯变换形成一个极大收敛群。这完成了莫比乌斯群作为作用于球面的极大收敛群的特征。在此之前，Gehring和Martin已经证明了莫比乌斯群在维度大于1的球面上的极大性。双曲平面的等距（共形）群作为一致拟等距群、一致拟共形群和作为其中每个元素拓扑共轭于等距的收敛群的极大性可以被视为推论。
英文摘要：
We investigate the relationship between quasisymmetric and convergence groups acting on the circle. We show that the Möbius transformations of the circle form a maximal convergence group. This completes the characterization of the Möbius group as a maximal convergence group acting on the sphere. Previously, Gehring and Martin had shown the maximality of the Möbius group on spheres of dimension greater than one. Maximality of the isometry (conformal) group of the hyperbolic plane as a uniform quasi-isometry group, uniformly quasiconformal group, and as a convergence group in which each element is topologically conjugate to an isometry may be viewed as consequences.
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