Local rigidity of Schottky maps
HTML articles powered by AMS MathViewer
- by Sergei Merenkov PDF
- Proc. Amer. Math. Soc. 142 (2014), 4321-4332 Request permission
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.References
- Mario Bonk, Bruce Kleiner, and Sergei Merenkov, Rigidity of Schottky sets, Amer. J. Math. 131 (2009), no. 2, 409–443. MR 2503988, DOI 10.1353/ajm.0.0045
- Guy David and Stephen Semmes, Fractured fractals and broken dreams, Oxford Lecture Series in Mathematics and its Applications, vol. 7, The Clarendon Press, Oxford University Press, New York, 1997. Self-similar geometry through metric and measure. MR 1616732
- Sergei Merenkov, Planar relative Schottky sets and quasisymmetric maps, Proc. Lond. Math. Soc. (3) 104 (2012), no. 3, 455–485. MR 2900233, DOI 10.1112/plms/pdr038
- R. L. Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925), no. 4, 416–428. MR 1501320, DOI 10.1090/S0002-9947-1925-1501320-8
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
- Email: smerenkov@ccny.cuny.edu
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 4321-4332
- MSC (2010): Primary 52C25
- DOI: https://doi.org/10.1090/S0002-9939-2014-12234-9
- MathSciNet review: 3267000