Arkiv för Matematik

, Volume 40, Issue 1, pp 1–26 | Cite as

Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture

  • Christopher J. Bishop


We show that proving the conjectured sharp constant in a theorem of Dennis Sullivan concerning convex sets in hyperbolic 3-space would imply the Brennan conjecture. We also prove that any conformal mapf:D→Ω can be factored as aK-quasiconformal self-map of the disk (withK independent of Ω) and a mapg:D→Ω with derivative bounded away from zero. In particular, there is always a Lipschitz homeomorphism from any simply connected Ω (with its internal path metric) to the unit disk.


Convex Hull Unit Disk Sharp Constant Internal Path Lipschitz Homeomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Institut Mittag-Leffler 2002

Authors and Affiliations

  • Christopher J. Bishop
    • 1
  1. 1.Mathematics DepartmentState University of New York at Stony BrookStony BrookUSA

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