Goodman, Oliver A. (1989) Metrized laminations and quasisymmetric maps. PhD thesis, University of Warwick.

Preview

PDF WRAP_Theses_Goodman_1989.pdf - Submitted Version - Requires a PDF viewer. Download (1671Kb) | Preview

Request Changes to record.

Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Teichmüller spaces, Earthquakes -- Mathematics, Metric spaces, Hyperbolic spaces, Quasiconformal mappings
Official Date:	June 1989
Dates:	Date Event June 1989 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Epstein, D. B. A.
Format of File:	pdf
Extent:	57 leaves : illustrations, charts
Language:	eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads