Continuity of Convex Hull Boundaries

  title={Continuity of Convex Hull Boundaries},
  author={Linda Keen},
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… CONTINUE READING

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