Extremal Kleinian groups
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- by William Abikoff and William J. Harvey PDF
- Proc. Amer. Math. Soc. 140 (2012), 267-278 Request permission
Abstract:
In 1967, Lipman Bers proved his area inequalities for Kleinian groups and gave examples to show that they are sharp; a group for which equality holds is termed extremal. Maskit’s work on function groups published during the next decade contained implicitly a characterization of all extremal groups for the second inequality.
Here we determine the class of extremal groups for the first area inequality: these maximal area groups are all torsion-free Schottky or almost Schottky groups. For completeness, we also show that any extremal group for the second area inequality is either quasi-Fuchsian or a regular b-group.
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Additional Information
- William Abikoff
- Affiliation: Department of Mathematics, University of Connecticut at Storrs, Storrs, Connecticut 06269-3009
- Email: abikoff@math.uconn.edu
- William J. Harvey
- Affiliation: Department of Mathematics, King’s College, Strand, London, WC2R-2LS England
- Email: Bill.Harvey@kcl.ac.uk
- Received by editor(s): May 14, 2010
- Received by editor(s) in revised form: November 13, 2010
- Published electronically: May 26, 2011
- Communicated by: Michael Wolf
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 267-278
- MSC (2010): Primary 30F40; Secondary 20H15
- DOI: https://doi.org/10.1090/S0002-9939-2011-10923-7
- MathSciNet review: 2833539