Convergence of Circle Packings in Euclidean Plane Público

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

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

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