dc.creator | Mirani, Mozhgan | |
dc.date.accessioned | 2020-08-22T00:04:53Z | |
dc.date.available | 2007-04-12 | |
dc.date.issued | 2006-04-12 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-03272006-143429 | |
dc.identifier.uri | http://hdl.handle.net/1803/11484 | |
dc.description.abstract | In this paper it is established that there is a faithful functor E from the category T whose objects are locally finite classical trees of minimal vertex degree three and whose morphisms are classes of quasi-isometries to the category U whose objects are perfect compact ultrametric spaces and whose morphisms are bi-Hölder homeomorphisms.
The image of morphisms under E are also quasi-conformal. If two quasi-conformal homeomorphisms are images of a morphisms under the functor E, their composition is also a quasi-conformal homeomorphism.
It is not known in more general cases
exactly when quasi-conformal homeomorphisms are closed under composition. Quasi-conformal homeomorphisms are studied in great depth and numerous examples of quasi-conformal homeomorphisms are given. Examples are also provided that show that compositions of quasi-conformal homeomorphisms need not be quasi-conformal. | |
dc.format.mimetype | application/pdf | |
dc.subject | ultrametric spaces | |
dc.subject | quasi-conformal homeomorphisms | |
dc.subject | Topology | |
dc.subject | category | |
dc.title | Classical Trees and Ultrametric Spaces | |
dc.type | dissertation | |
dc.contributor.committeeMember | Michael L. Mihalik | |
dc.contributor.committeeMember | John G. Ratcliffe | |
dc.contributor.committeeMember | Guoliang Yu | |
dc.contributor.committeeMember | Thomas W. Kephart | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2007-04-12 | |
local.embargo.lift | 2007-04-12 | |
dc.contributor.committeeChair | Bruce Hughes | |