## Institute for Mathematical Sciences

## Preprint ims90-16

** L. Keen and C. Series **
* Continuity of Convex Hull Boundaries *

Abstract: In this paper we consider families of finitely generatedKleinian groups {G_{μ}} that depend holomorphically on a
parameter μ which varies in an arbitrary connected domain
in *C*. The groups G_{μ} are quasiconformally conjugate.
We denote the boundary of the convex hull of the
limit set of G\EC by ∂*C*{G_{μ}). The quotient ∂*C*(G_{μ})/G_{μ} is
a union of pleated surfaces each carrying a hyperbolic
structure. We fix our attention on one component *S*_{μ}
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 *S*_{μ} are continuous
functions of μ.

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