Book Review
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MathSciNet review:
2729896
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Book Information:
Title:
Hyperbolic geometry from a local viewpoint
Additional book information:
Linda Keen and Nikola Lakic,
London Mathematical Society Student Texts 68, Cambridge University Press,
2007,
x+271 pp.,
ISBN 978-0-521-86360-5,
US $121.00$,
hardback
Lars V. Ahlfors, Conformal invariants: topics in geometric function theory, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0357743
Alan F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, vol. 91, Springer-Verlag, New York, 1983. MR 698777, DOI 10.1007/978-1-4612-1146-4
A. F. Beardon, T. K. Carne, D. Minda, and T. W. Ng, Random iteration of analytic maps, Ergodic Theory Dynam. Systems 24 (2004), no. 3, 659–675. MR 2060992, DOI 10.1017/S0143385704000033
4. L. Bers.
Collected Works, Part II.
AMS, Providence, R. I., 2000.
Peter Buser, The collar theorem and examples, Manuscripta Math. 25 (1978), no. 4, 349–357. MR 509590, DOI 10.1007/BF01168048
Frederick P. Gardiner, Teichmüller theory and quadratic differentials, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1987. A Wiley-Interscience Publication. MR 903027
7. F. P. Gardiner and N. Lakic.
Quasiconformal Teichmüller Theory.
AMS, Providence, Rhode Island, 2000.
Linda Keen, Canonical polygons for finitely generated Fuchsian groups, Acta Math. 115 (1965), 1–16. MR 183873, DOI 10.1007/BF02392200
Linda Keen, Collars on Riemann surfaces, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973) Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N.J., 1974, pp. 263–268. MR 0379833
Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
Irwin Kra, The Carathéodory metric on abelian Teichmüller disks, J. Analyse Math. 40 (1981), 129–143 (1982). MR 659787, DOI 10.1007/BF02790158
12. B. Maskit.
Kleinian Groups.
Springer-Verlag, New York, 1987.
Katsuhiko Matsuzaki and Masahiko Taniguchi, Hyperbolic manifolds and Kleinian groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1998. Oxford Science Publications. MR 1638795
Curtis T. McMullen, Complex dynamics and renormalization, Annals of Mathematics Studies, vol. 135, Princeton University Press, Princeton, NJ, 1994. MR 1312365
John Milnor, Dynamics in one complex variable, 3rd ed., Annals of Mathematics Studies, vol. 160, Princeton University Press, Princeton, NJ, 2006. MR 2193309
Zeev Nehari, Conformal mapping, Dover Publications, Inc., New York, 1975. Reprinting of the 1952 edition. MR 0377031
17. H. Poincaré.
Theory of Fuchsian Groups, Papers on Fuchsian Functions.
Springer-Verlag, 1985.
- 1.
- L. V. Ahlfors.
Conformal Invariants: Topics in Geometric Function Theory.
McGraw-Hill, New York, 1973. MR 0357743
- 2.
- A. Beardon.
The Geometry of Discrete Groups.
Graduate Texts in Mathematics. Springer-Verlag, New York, Berlin, 1983. MR 0698777
- 3.
- A. Beardon, T. Carne, D. Minda, and P. Ng.
Random iteration of analytic maps.
Erg. Th. & Dyn. Sys., 24(3):659-675, 2004. MR 2060992
- 4.
- L. Bers.
Collected Works, Part II.
AMS, Providence, R. I., 2000.
- 5.
- P. Buser.
The collar theorem and examples.
Manuscripta Math., 25:349-357, 1978. MR 0509590
- 6.
- F. P. Gardiner.
Teichmüller Theory and Quadratic Differentials.
John Wiley & Sons, New York, 1987. MR 0903027
- 7.
- F. P. Gardiner and N. Lakic.
Quasiconformal Teichmüller Theory.
AMS, Providence, Rhode Island, 2000.
- 8.
- L. Keen.
Canonical polygons for finitely generated Fuchsian groups.
Acta Math., 115:1-16, 1966. MR 0183873
- 9.
- L. Keen.
Collars on Riemann surfaces.
Ann Math. Studies, 79:263-268, 1974. MR 0379833
- 10.
- S. Kobayashi.
Hyperbolic Manifolds and Holomorpic Mappings.
Marcel Dekker, New York, 1970. MR 0277770
- 11.
- I. Kra.
The Carathéodory metric on abelian Teichmüller disks.
J. Analyse Math., 40:129-143, 1981. MR 0659787
- 12.
- B. Maskit.
Kleinian Groups.
Springer-Verlag, New York, 1987.
- 13.
- K. Matsuzaki and M. Taniguchi.
Hyperbolic Manifolds and Kleinian Groups.
Oxford Mathematical Monographs, Oxford University Press, 1998. MR 1638795
- 14.
- C. T. McMullen.
Complex Dynamics and Renormalization, volume 135 of Ann. of Math. Studies.
Princeton Univ. Press, 1996, 1994. MR 1312365
- 15.
- J. Milnor.
Dynamics in One Complex Variable: Introductory Lectures.
Princeton Univ. Press, Princeton, N. J., 2006. MR 2193309
- 16.
- Z. Nehari.
Conformal Mapping.
Dover Publications, New York, 1975. MR 0377031
- 17.
- H. Poincaré.
Theory of Fuchsian Groups, Papers on Fuchsian Functions.
Springer-Verlag, 1985.
Review Information:
Reviewer:
Frederick P. Gardiner
Affiliation:
Brooklyn College, CUNY, Bedford Avenue and Avenue H, Brooklyn, New York 11210
Email:
frederick.gardiner@gmail.com
Journal:
Bull. Amer. Math. Soc.
46 (2009), 363-368
DOI:
https://doi.org/10.1090/S0273-0979-08-01236-6
Published electronically:
November 20, 2008
Review copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
