Published May 5, 2017
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Extremal maps of the universal hyperbolic solenoid
Abstract
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.
Additional Information
The third author was partially supported by NSF grant DMS-0505652.Attached Files
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Additional details
- Eprint ID
- 77237
- Resolver ID
- CaltechAUTHORS:20170505-144834084
- DMS-0505652
- NSF
- Created
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2017-05-05Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field