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Title: Metrized laminations and quasisymmetric maps
Author: Goodman, Oliver A.
ISNI:       0000 0001 3505 0727
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1989
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Teichmuller space is defined as a space of hyperbolic structures on a surface rather than as a space of conformal structures. Earthquakes are defined and we see how they correspond to hyperbolic structures, via homeomorphisms of the circle. Metrised laminations are defined and we obtain a correspondence with earthquakes. We deduce a correspondence between measured laminations and earthquakes. We define uniform boundedness of earthquakes and show that such earthquakes are surjective. Quasisymmetric maps are defined and investigated. We show that an earthquake is uniformly bounded if and only if its boundary mapping is quasisymmetric. Finally we show how a uniformly bounded earthquake can be approximated, in a natural fashion, by a bi-Lipechits diffeomorphism.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics