Kim, Daniel Min2016-11-152016-11-152016-11-14vt_gsexam:9218http://hdl.handle.net/10919/73446A 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.ETDIn CopyrightNearly Euclidean Thurston mapshalf-space theoremThesis