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CONTINUITY OF CONVEX-HULL BOUNDARIES
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UNSPECIFIED (1995) CONTINUITY OF CONVEX-HULL BOUNDARIES. PACIFIC JOURNAL OF MATHEMATICS, 168 (1). pp. 183-206. ISSN 0030-8730.
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Abstract
In this paper we consider families of finitely generated Kleinian groups {G(mu)} that depend holomorphically on a parameter mu which varies in an arbitrary connected domain in C. The groups G(mu) are quasiconformally conjugate. We denote the boundary of the convex hull of the limit set of G(mu) by partial derivative C(G(mu)). The quotient partial derivative C(G(mu))/G(mu) is a union of pleated surfaces each carrying a hyperbolic structure. We fix our attention on one component S-mu and we address the problem of how it varies with mu. We prove that both the hyperbolic structure and the bending measure of the pleating lamination of S-mu are continuous functions of mu.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | PACIFIC JOURNAL OF MATHEMATICS | ||||
Publisher: | PACIFIC JOURNAL MATHEMATICS | ||||
ISSN: | 0030-8730 | ||||
Official Date: | March 1995 | ||||
Dates: |
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Volume: | 168 | ||||
Number: | 1 | ||||
Number of Pages: | 24 | ||||
Page Range: | pp. 183-206 | ||||
Publication Status: | Published |
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