Some remarks on bounded earthquakes
HTML articles powered by AMS MathViewer
- by Dragomir Šarić PDF
- Proc. Amer. Math. Soc. 138 (2010), 871-879 Request permission
Abstract:
We show that an earthquake of a geometrically infinite hyperbolic surface induces an asymptotically conformal change in the hyperbolic metric if and only if the measured lamination associated with the earthquake is asymptotically trivial on the surface. Then we show that the contraction along earthquake paths is continuous in the Teichmüller space of any hyperbolic surface. Finally, we show that if a measured lamination vanishes while approaching infinity at a rate higher than the distance to the boundary, then it must be trivial.References
- Adrien Douady and Clifford J. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986), no. 1-2, 23–48. MR 857678, DOI 10.1007/BF02392590
- Clifford J. Earle, Frederick P. Gardiner, and Nikola Lakic, Asymptotic Teichmüller space. II. The metric structure, In the tradition of Ahlfors and Bers, III, Contemp. Math., vol. 355, Amer. Math. Soc., Providence, RI, 2004, pp. 187–219. MR 2145063, DOI 10.1090/conm/355/06452
- Clifford J. Earle, Vladimir Markovic, and Dragomir Saric, Barycentric extension and the Bers embedding for asymptotic Teichmüller space, Complex manifolds and hyperbolic geometry (Guanajuato, 2001) Contemp. Math., vol. 311, Amer. Math. Soc., Providence, RI, 2002, pp. 87–105. MR 1940165, DOI 10.1090/conm/311/05448
- D. B. A. Epstein, A. Marden, and V. Markovic, Quasiconformal homeomorphisms and the convex hull boundary, Ann. of Math. (2) 159 (2004), no. 1, 305–336. MR 2052356, DOI 10.4007/annals.2004.159.305
- F. P. Gardiner, J. Hu, and N. Lakic, Earthquake curves, Complex manifolds and hyperbolic geometry (Guanajuato, 2001) Contemp. Math., vol. 311, Amer. Math. Soc., Providence, RI, 2002, pp. 141–195. MR 1940169, DOI 10.1090/conm/311/05452
- Frederick P. Gardiner and Dennis P. Sullivan, Symmetric structures on a closed curve, Amer. J. Math. 114 (1992), no. 4, 683–736. MR 1175689, DOI 10.2307/2374795
- Jun Hu, Earthquake measure and cross-ratio distortion, In the tradition of Ahlfors and Bers, III, Contemp. Math., vol. 355, Amer. Math. Soc., Providence, RI, 2004, pp. 285–308. MR 2145070, DOI 10.1090/conm/355/06459
- Steven P. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983), no. 2, 235–265. MR 690845, DOI 10.2307/2007076
- Dragomir Šarić, Real and complex earthquakes, Trans. Amer. Math. Soc. 358 (2006), no. 1, 233–249. MR 2171231, DOI 10.1090/S0002-9947-05-03651-2
- Dragomir Šarić, Bounded earthquakes, Proc. Amer. Math. Soc. 136 (2008), no. 3, 889–897. MR 2361861, DOI 10.1090/S0002-9939-07-09146-0
- William P. Thurston, Earthquakes in two-dimensional hyperbolic geometry, Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984) London Math. Soc. Lecture Note Ser., vol. 112, Cambridge Univ. Press, Cambridge, 1986, pp. 91–112. MR 903860
- William P. Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series, vol. 35, Princeton University Press, Princeton, NJ, 1997. Edited by Silvio Levy. MR 1435975, DOI 10.1515/9781400865321
Additional Information
- Dragomir Šarić
- Affiliation: Department of Mathematics, Queens College of The City University of New York, 65-30 Kissena Boulevard, Flushing, New York 11367
- Email: Dragomir.Saric@qc.cuny.edu
- Received by editor(s): September 10, 2008
- Published electronically: October 21, 2009
- Additional Notes: This work was in part supported by PSC CUNY grant PSC-REG-39-386.
- Communicated by: Mario Bonk
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 871-879
- MSC (2010): Primary 30F60; Secondary 32G15
- DOI: https://doi.org/10.1090/S0002-9939-09-10156-9
- MathSciNet review: 2566553