The logarithmic spiral: A counterexample to the K = 2 conjecture

Annals of Mathematics

Volumn 161, Issue 2, 2005, Pages 925-957

  Epstein, D B A ^a   Markovic, V ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23844548378     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2005.161.925     Document Type: Article

References (19)

1. L. V. AHLFORS, Lectures on Quasiconformal Mappings, Van Nostrand Math. Studies 10, D. Van Nostrand, Co., Inc., New York, 1966.
2. A. BEURLING and L. AHLFORS, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125-142.
3. C. J. BISHOP, An explicit constant for Sullivan's convex hull theorem, In the Tradition of Ahlfors and Bers, III Proc. Ahlfors-Bers Colloq. (Storrs, CT, 2001) (W. Abikoff and A. Haas, eds), Contemp. Math. 355, 41-69, A.M.S., Providence, RI, 2004.
4. _, Bilipschitz approximations of quasiconformal maps, Ann. Acad. Sci. Fenn. 27 (2002), 97-108.
5. _, Divergence groups have the Bowen property, Ann. of Math. 154 (2001), 205-217.
6. _, Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture, Ark. Math. 40 (2002), 1-26.
7. M. BRIDGEMAN, Average bending of convex pleated planes in hyperbolic three-space, Invent. Math. 132 (1998), 381-391.
8. R. D. CANARY, D. B. A. EPSTEIN, and P. GREEN, Notes on the notes of Thurston, in Analytical and Geometric Aspects of Hyperbolic Space (D.B.A. Epstein, ed.) (Coventry/Durham 1984), London Math. Soc. Lecture Note Ser. 111, 3-92, Cambridge Univ. Pres, Cambridge, 1987.
9. D. B. A. EPSTEIN and A. MARDEN, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, in Analytical and Geometric Aspects of Hyperbolic Space (Coventry/Durham 1984), London Math. Soc. Lecture Note Ser. 111, 113-253, Cambridge Univ. Press, Cambridge, 1987.
10. D. B. A. EPSTEIN, A. MARDEN, and V. MARKOVIC, Quasiconformal homeomorphisms and the convex hull boundary, Ann. of Math. 159 (2004), 305-336.
11. _, Convex regions in ℂ and their domes, Proc. L.M.S., to appear.
12. _, Complex earthquakes and deformations of the unit disk, preprint, 2004.
13. R. FEHLMAN, Ueber extremale quasikonforme abbildungnen, Comment. Math. Helv. 56 (1981), 558-580.
14. N. LAKIC, Substantial boundary points for plane domains and Gardiner's conjecture, Ann. Acad. Sci. Fenn. 25 (2000), 285-306.
15. O. LEHTO and K. I. VIRTANEN, Quasiconformal Mappings in the Plane, 2nd edition, Springer-Verlag, New York, 1973.
16. E. REICH, Extremal quasiconformal mappings of the disk (R. Kühnau, ed.) in Geometric Function Theory, Vol. 1, Handbook of Complex Analysis, Elsevier Scientific Publ., Co., New York, 2001.
17. K. STREBEL, On the existence of extremal Teichmüller mappings, J. d'Anal Math. 30 (1976), 441-447.
18. 1, Lecture Notes in Math. 842, Springer-Verlag, New York, 1981.
19. W. P. THURSTON, Hyperbolic structure on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle; available at http://arXiv.org under arXiv:math.GT/9801045.