Nearly Euclidean Thurston Maps and the Halfspace Theorem

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2016

Author dc:creator

• Kim, Daniel Min

Chair dc:contributor.committeechair

• Floyd, William J.

Committee members dc:contributor.committeemember

• Brown, Ezra A.
• Rossi, John F.

• Nearly Euclidean Thurston maps
• half-space theorem

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:9218

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/73446