Canonical Thurston obstructions for subhyperbolic semirational branched coverings
Authors:
Tao Chen and Yunping Jiang
Journal:
Conform. Geom. Dyn. 17 (2013), 625
MSC (2010):
Primary 37F30, 37F20, 37F10, 30F30
Published electronically:
January 23, 2013
MathSciNet review:
3010347
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We prove that the canonical Thurston obstruction for a subhyper bolic semirational branched covering exists if the branched covering is not CLHequivalent to a rational map.
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 [CJS1]
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 [CJS2]
 G. Cui, Y. Jiang and D. Sullivan, On geometrically finite branched covering mapsII. Realization of rational maps, Complex Dynamics and Related Topics, New Studies in Advanced Mathematics, 2004, The International Press, 1529. MR 2504308 (2011c:37093)
 [CJ]
 Guizhen Cui and Yunping Jiang, Geometrically finite and semirational branched coverings of the twosphere, Trans. Amer. Math. Soc. 363 (2011), no. 5, 27012714. MR 2763733 (2012e:37090), http://dx.doi.org/10.1090/S000299472010052110
 [CT]
 Guizhen Cui and Lei Tan, A characterization of hyperbolic rational maps, Invent. Math. 183 (2011), no. 3, 451516. MR 2772086 (2012c:37088), http://dx.doi.org/10.1007/s0022201002818
 [DH]
 Adrien Douady and John H. Hubbard, A proof of Thurston's topological characterization of rational functions, Acta Math. 171 (1993), no. 2, 263297. MR 1251582 (94j:58143), http://dx.doi.org/10.1007/BF02392534
 [EM]
 Clifford J. Earle and Sudeb Mitra, Variation of moduli under holomorphic motions, In the tradition of Ahlfors and Bers (Stony Brook, NY, 1998) Contemp. Math., vol. 256, Amer. Math. Soc., Providence, RI, 2000, pp. 3967. MR 1759669 (2001f:30031), http://dx.doi.org/10.1090/conm/256/03996
 [GJW]
 Frederick P. Gardiner, Yunping Jiang, and Zhe Wang, Holomorphic motions and related topics, Geometry of Riemann surfaces, London Math. Soc. Lecture Note Ser., vol. 368, Cambridge Univ. Press, Cambridge, 2010, pp. 156193. MR 2665009 (2011j:37087)
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 F. R. Gantmacher, Theory of matrices. Chelsea, 1959. MR 1657129 (99f:15001)
 [Ji]
 Y. Jiang, A framework towards understanding the characterization of holomorphic maps, to appear in Frontiers in Complex Dynamics, Princeton, 2013.
 [JMW]
 Yunping Jiang, Sudeb Mitra, and Zhe Wang, Liftings of holomorphic maps into Teichmüller spaces, Kodai Math. J. 32 (2009), no. 3, 547563. MR 2582017 (2010m:32015), http://dx.doi.org/10.2996/kmj/ 1257948895
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Additional Information
Tao Chen
Affiliation:
Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York, New York 10016
Email:
chentaofdh@gmail.com
Yunping Jiang
Affiliation:
Department of Mathematics, Queens College of CUNY, 6530 Kissena Blvd, Flushing, NY 11367 and Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York, New York 10016
Email:
yunping.jiang@qc.cuny.edu
DOI:
http://dx.doi.org/10.1090/S108841732013002506
PII:
S 10884173(2013)002506
Received by editor(s):
March 19, 2012
Published electronically:
January 23, 2013
Additional Notes:
The second author is partially supported by the collaboration grant (#199837) from the Simons Foundation, the CUNY collaborative incentive research grant (#1861), and awards from PSCCUNY. This research is also partially supported by the collaboration grant (#11171121) from the NSF of China and a collaboration grant from the Academy of Mathematics and Systems Science and the Morningside Center of Mathematics at the Chinese Academy of Sciences.
Article copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
