Generalized discrete Schwarz-Pick lemma for circle packings

Author

Jeffrey Alan Van Eeuwen

Date of Award

5-1992

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Kenneth R. Stephenson

Committee Members

John Conway, Stefan Richter

Abstract

In a paper titled "The Schwarz-Pick Lemma for Circle Packings," Alan Beardon and Kenneth Stephenson proved a discrete analogue of the classical Schwarz-Pick Lemma for circle packings. This paper generalizes this discrete analogue. The circle packings considered by Beardon and Stephenson are restricted in that neighboring circles have overlap angles equal to zero (i.e. neighboring circles are tangent). This restriction is lifted to allow neighboring circles to have overlap angles between 0 and π/2. Also included is a proof, that is independent of Andreev's work, of the existence of circle packings of triangulations of the closed disc in the hyperbolic plane with prescribed overlap angles.

Recommended Citation

Van Eeuwen, Jeffrey Alan, "Generalized discrete Schwarz-Pick lemma for circle packings. " Master's Thesis, University of Tennessee, 1992.
https://trace.tennessee.edu/utk_gradthes/12301