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Book Review
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Book Information
Author(s):
Kenneth Stephenson
Title:
Introduction to circle packing: The theory of discrete analytic functions
Additional book information:
Cambridge University Press,
Cambridge,
2005,
xii+356 pp.,
£42,
ISBN 978-0-521-82356-2
References:
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- 3.
- A.F. Beardon and K. Stephenson, The uniformization theorem for circle packings, Indiana Univ. Math. J. 39 (1990), 1383-1425. MR 1087197 (92b:52038)
- 4.
- A.F. Beardon and K. Stephenson, The Schwarz-Pick lemma for circle packings, Ill. J. Math. 35 (1991), 577-606. MR 1115988 (93a:30028a)
- 5.
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- 6.
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- M. Bonk and B. Kleiner, Quasisymmetric parametrizations of two-dimensional metric spheres, Invent. Math. 150 (2002), no. 1, 127-183. MR 1930885 (2004k:53057)
- 8.
- M. Bonk and B. Kleiner, Conformal dimension and Gromov hyperbolic groups with
 -sphere boundary, Geometry & Topology 9 (2005), 219-246. MR 2116315 (2005k:20102) - 9.
- P.L. Bowers and K. Stephenson, Circle packings in surfaces of finite type: An in situ approach with applications to moduli, Topology 32 (1993), 157-183. MR 1204413 (94d:30083)
- 10.
- P.L. Bowers and K. Stephenson, A ``regular'' pentagonal tiling of the plane, Con. Geom. and Dynamics 1 (1997), 58-86. MR 1479069 (99d:52016)
- 11.
- P.L. Bowers and K. Stephenson, Uniformizing dessins and Belyĭ maps via circle packing, Mem. Amer. Math. Soc. 170 (2004), no. 805, xii+97 pp. MR 2053391 (2005a:30068)
- 12.
- J.W. Cannon, The combinatorial Riemann mapping theorem, Acta. Math. 173 (1994), 155-234. MR 1301392 (95k:30046)
- 13.
- J.W. Cannon, W.J. Floyd, and W.R. Parry, ``Squaring rectangles: the finite Riemann mapping theorem, in The Mathematical Heritage of Wilhelm Magnus--Groups, Geometry, and Special Functions'', Contemporary Mathematics, vol. 169, Amer. Math. Soc., Providence, 1994, pp. 133-212. MR 1292901 (95g:20045)
- 14.
- J.W. Cannon, W.J. Floyd, and W.R. Parry, The length-area method and discrete Riemann mappings, unpublished manuscript available from Bill Floyd that is based on a talk given by J. Cannon at the Ahlfors Celebration at Stanford University in September, 1997 (1998).
- 15.
- M. Gromov, ``Hyperbolic Groups'', in Essays in Group Theory, G.M. Gersten, ed., MSRI Publ. 8, 1987, pp. 75-263. MR 919829 (89e:20070)
- 16.
- M. Gromov, ``Asymptotic invariants of infinite groups'', in Geometric Group Theory, Vol. 2 (Sussex, 1991), LMS Lecture Note Series, 182, Cambridge University Press, Cambridge, 1993, pp. 1-295 MR 1253544 (95m:20041)
- 17.
- R. Hamilton, Three-manifolds with positive Ricci curvature, J. Diff. Geom. 17 (1982), 255-306. MR 664497 (84a:53050)
- 18.
- Z.-X. He and O. Schramm, Fixed points, Koebe uniformization and circle packings, Annals of Math. 137 (1993), 369-406. MR 1207210 (96b:30015)
- 19.
- M.K. Hurdal and K. Stephenson, Cortical cartography using the discrete conformal approach of circle packings, NeuroImage 23 (2004), Supplement 1, S119-S128.
- 20.
- P. Koebe, Kontaktprobleme der Konformen Abbildung, Ber. Sächs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 88 (1936), 141-164.
- 21.
- B. Rodin and D. Sullivan, The convergence of circle packings to the Riemann mapping, J. Diff. Geom. 26 (1987), 349-360. MR 906396 (90c:30007)
- 22.
- O. Schramm, Square tilings with prescribed combinatorics, Israel J. Math. 84 (1993), 97-118. MR 1244661 (94h:52045)
- 23.
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Additional Information:
Reviewer(s):
Philip
L.
Bowers
Affiliation:
Department of Mathematics, The Florida State University, 1017 Academic Way, Tallahassee, Florida 32306-4510
Email:
bowers@math.fsu.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
46
(2009),
511-525.
MSC
(2000):
Primary 52C26
DOI:
10.1090/S0273-0979-09-01245-2
PII:
S 0273-0979(09)01245-2
Posted:
February 19, 2009
Additional notes:
This review is dedicated to the memory of Oded Schramm, who worked in circle packing before his discovery of stochastic Loewner evolution and its applications to critical phenomena. This extraordinary mathematician's untimely death on 01 September 2008 in a hiking accident was a great loss for our community.
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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