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Extremal maps of the universal hyperbolic solenoid

Epstein, Adam and Markovic, Vladimir and Šarić, Dragomir (2006) Extremal maps of the universal hyperbolic solenoid. . (Submitted)

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We show that the set of points in the Teichmuller space of the universal hyperbolic solenoid which do not have a Teichmuller extremal representative is generic (that is, its complement is the set of the first kind in the sense of Baire). This is in sharp contrast with the Teichmuller space of a Riemann surface where at least an open, dense subset has Teichmuller extremal representatives. In addition, we provide a sufficient criteria for the existence of Teichmuller extremal representatives in the given homotopy class. These results indicate that there is an interesting theory of extremal (and uniquely extremal) quasiconformal mappings on hyperbolic solenoids.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:The third author was partially supported by NSF grant DMS-0505652.
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Record Number:CaltechAUTHORS:20170505-144834084
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77237
Deposited By: Tony Diaz
Deposited On:05 May 2017 22:36
Last Modified:03 Oct 2019 17:55

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