Type of Document Dissertation Author Mirani, Mozhgan Author's Email Address email@example.com URN etd-03272006-143429 Title Classical Trees and Ultrametric Spaces Degree PhD Department Mathematics Advisory Committee
Advisor Name Title Bruce Hughes Committee Chair Guoliang Yu Committee Member John G. Ratcliffe Committee Member Michael L. Mihalik Committee Member Thomas W. Kephart Committee Member Keywords
- ultrametric spaces
- quasi-conformal homeomorphisms
Date of Defense 2006-03-01 Availability unrestricted AbstractIn 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.
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