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Local rigidity of Schottky maps

Author: Sergei Merenkov
Journal: Proc. Amer. Math. Soc. 142 (2014), 4321-4332
MSC (2010): Primary 52C25
Published electronically: August 13, 2014
MathSciNet review: 3267000
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Abstract: We introduce Schottky maps--conformal maps between relative Schottky sets--and study their local rigidity properties. This continues the investigations of relative Schottky sets initiated in the author's earlier work entitled Planar relative Schottky sets and quasisymmetric maps, Proc. Lond. Math. Soc. (3) 104 (2012), no. 3, 455-485. Besides being of independent interest, the latter and current works provide key ingredients in the forthcoming proof of quasisymmetric rigidity of Sierpiński carpet Julia sets of rational functions.

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Additional Information

Sergei Merenkov
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801
Address at time of publication: Department of Mathematics, The City College of New York, Convent Avenue at 138th Street, New York, New York 10031

Received by editor(s): January 22, 2012
Received by editor(s) in revised form: August 3, 2012, and January 16, 2013
Published electronically: August 13, 2014
Additional Notes: The author was supported by NSF grant DMS-1001144
Communicated by: Mario Bonk
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.