Continuity of convex hull boundaries
Continuity of convex hull boundaries
复制标题
凸包边界的连续性
DOI：
10.2140/pjm.1995.168.183
复制
发表时间：
1995
影响因子：
0.6
通讯作者：
C. Series
中科院分区：
文献类型：
--
作者：
L. Keen;C. Series
本文考虑一类全纯地依赖于参数μ在C中任意连通区域内变化的N-生成Kleinian群{Gμ}。群Gμ是拟共形共轭的。我们用dC（Gμ）表示Gμ的极限集的凸船体的边界。商dC（Gμ）/Gμ是每个带有双曲结构的褶曲面的并集。我们将注意力集中在一个分量Sμ上，并解决它如何随μ变化的问题。我们证明了Sμ的褶层的双曲结构和弯曲测度都是μ的连续函数。
In this paper we consider families of finitely generated Kleinian groups {Gμ} that depend holomorphically on a parameter μ which varies in an arbitrary connected domain in C. The groups Gμ are quasiconformally conjugate. We denote the boundary of the convex hull of the limit set of Gμ by dC{Gμ). The quotient dC(Gμ)/Gμ is a union of pleated surfaces each carrying a hyperbolic structure. We fix our attention on one component Sμ and we address the problem of how it varies with μ. We prove that both the hyperbolic structure and the bending measure of the pleating lamination of Sμ are continuous functions of μ.