A Thurston map whose postcritical set consists of exactly four points and for which the local degree at each of its critical points is 2 is called textit{nearly Euclidean}. These maps were specified to parse Thurston's combinatorial characterization of rational functions. We determine an extension of the half-space theorem which provides an open hyperbolic half-space such that the negative reciprocal of any fixed slope value is excluded from the boundary of the half-space. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/73446 |
| Date | 14 November 2016 |
| Creators | Kim, Daniel Min |
| Contributors | Mathematics, Floyd, William J., Brown, Ezra A., Rossi, John F. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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