Convergence of Circle Packings in Euclidean Plane Open Access

Abstract

In this paper, I want to present to the readers some basic knowledge about circle packing in the setting of Euclidean plane. Circle packing was introduced by William Thurston [8] in his lecture notes. I will establish the background on the discrete analytic function, which maps carriers of circle packings to carriers of circle packings and preserve the orientation and tangency. Last, I will present the proof of the Thurston's Conjecture on circle packings, which was proved by Burton Rodin and Dennis Sullivan [5], and is now called the Rodin-Sullivan Theorem.

Table of Contents

Table of Contents
1. Introduction...1
2. Introduction to Circle Packing...2
3. Conformal and Quasiconformal Mappings...12
4. Lemmas for the Main Theorem...21
5. Rodin-Sullivan Theorem...28
6. Reference...34

About this Honors Thesis

Rights statement

• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Emory College
Department	Mathematics
Degree	BS
Submission	Honors Thesis
Language	English
Research Field	Mathematics
Keyword	Circle Packing
Committee Chair / Thesis Advisor	Borthwick, David, Emory University
Committee Members	Yang, Shanshuang, Emory University Seitaridou, Effrosyni, Emory University

Last modified

Primary PDF

Thumbnail	Title	Date Uploaded	Actions
	Convergence of Circle Packings in Euclidean Plane ()	2018-08-28 10:08:33 -0400	Press to Select an action Download

Supplemental Files

Thumbnail	Title	Date Uploaded	Actions