Convergence of Circle Packings in Euclidean Plane Público

Wu, Xinhui (2013)

Permanent URL: https://etd.library.emory.edu/concern/etds/2v23vt451?locale=pt-BR
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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

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