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Some remarks on bounded earthquakes
Author(s):
Dragomir
Saric
Journal:
Proc. Amer. Math. Soc.
MSC (2010):
Primary 30F60;
Secondary 32G15
Posted:
October 21, 2009
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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:
-
- 1.
- A. Douady and C. J. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986), no. 1-2, 23-48. MR 857678 (87j:30041)
- 2.
- C. Earle, F. Gardiner and N. Lakic, Asymptotic Teichmüller space. II. The metric structure, In the tradition of Ahlfors and Bers, III, 187-219, Contemp. Math., 355, Amer. Math. Soc., Providence, RI, 2004. MR 2145063 (2006g:30078)
- 3.
- C. Earle, V. Markovic and D. Šarić, Barycentric extension and the Bers embedding for asymptotic Teichmüller space, Complex manifolds and hyperbolic geometry (Guanajuato, 2001), 87-105, Contemp. Math., 311, Amer. Math. Soc., Providence, RI, 2002. MR 1940165 (2003i:30072)
- 4.
- D. 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 (2005d:30067)
- 5.
- F. Gardiner, J. Hu and N. Lakic, Earthquake curves, Complex manifolds and hyperbolic geometry (Guanajuato, 2001), 141-195, Contemp. Math., 311, Amer. Math. Soc., Providence, RI, 2002. MR 1940169 (2003i:37033)
- 6.
- F. Gardiner and D. Sullivan, Symmetric structures on a closed curve, Amer. J. Math. 114 (1992), no. 4, 683-736. MR 1175689 (95h:30020)
- 7.
- J. Hu, Earthquake measure and cross-ratio distortion, In the tradition of Ahlfors and Bers, III, 285-308, Contemp. Math., 355, Amer. Math. Soc., Providence, RI, 2004. MR 2145070 (2006m:37056)
- 8.
- S. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983), no. 2, 235-265. MR 690845 (85e:32029)
- 9.
- D. Šarić, Real and complex earthquakes, Trans. Amer. Math. Soc. 358 (2006), no. 1, 233-249. MR 2171231 (2006i:30063)
- 10.
- D. Šarić, Bounded earthquakes, Proc. Amer. Math. Soc. 136 (2008), no. 3, 889-897 (electronic). MR 2361861 (2009f:30101)
- 11.
- W. Thurston, Earthquakes in two-dimensional hyperbolic geometry, Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984), 91-112, London Math. Soc. Lecture Note Ser., 112, Cambridge Univ. Press, Cambridge, 1986. MR 903860 (88m:57015)
- 12.
- W. Thurston, Three-dimensional geometry and topology, Vol. 1. Edited by Silvio Levy. Princeton Mathematical Series, 35. Princeton University Press, Princeton, NJ, 1997. MR 1435975 (97m:57016)
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Additional Information:
Dragomir
Saric
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
DOI:
10.1090/S0002-9939-09-10156-9
PII:
S 0002-9939(09)10156-9
Received by editor(s):
September 10, 2008
Posted:
October 21, 2009
Additional Notes:
This work was in part supported by PSC CUNY grant PSC-REG-39-386.
Communicated by:
Mario Bonk
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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