Introduction to Circle Packing

The Theory of Discrete Analytic Functions

Kenneth Stephenson

370 pages, parution le 15/06/2005

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Indisponible

Résumé

The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest. This book lays the foundation for a topic with wide appeal and a bright future.

Foundational: this is the first book on a fascinating new topic and it lays out a clear formulation from definitions to applications
Accessible: it has four parts with increasing sophistication, accompanied by numerous illustrations
There are seven appendices on stand-alone topics which are widely accessible and suitable for independent projects

Sommaire

I An overview of circle packing
- 1 A circle packing menagerie
- 2 Circle packings in the wild
II Rigidity : maximal packings
- 3 Preliminaries : topology, combinatorics, and geometry
- 4 Statement of the fundamental result
- 5 Bookkeeping and monodromy
- 6 Proof for combinatorial closed discs
- 7 Proof for combinatorial spheres
- 8 Proof for combinatorial open discs
- 9 Proof for combinatorial surfaces
III Flexibility : analytic functions
- 10 The intuitive landscape
- 11 Discrete analytic functions
- 12 Construction tools
- 13 Discrete analytic functions on the disc
- 14 Discrete entire functions
- 15 Discrete rational functions
- 16 Discrete analytic functions on Riemann surfaces
- 17 Discrete conformal structure
- 18 Random walks on circle packings
IV Resolution : approximation
- 19 Thurston's conjecture
- 20 Extending the Rodin-Sullivan theorem
- 21 Approximation of analytic functions
- 22 Approximation of conformal structures
- 23 Applications
- App. A Primer on classical complex analysis
- App. B The ring lemma
- App. C Doyle spirals
- App. D The Brooks parameter
- App. E Inversive distance packings
- App. F Graph embedding
- App. G Square grid packings
- App. H Schwarz and buckyballs
- App. I CirclePack

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Kenneth Stephenson
Parution	15/06/2005
Nb. de pages	370
Format	18 x 26
Couverture	Relié
Poids	930g
Intérieur	Noir et Blanc
EAN13	9780521823562
ISBN13	978-0-521-82356-2