Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


MathSciNet review: 2952711
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Simon Donaldson
Title: Riemann surfaces
Additional book information: Oxford Graduate Texts in Mathematics, Vol. 22, Oxford University Press, Oxford, 2011, xiv+286 pp., ISBN 978-0-19-960674-0

References [Enhancements On Off] (What's this?)

  • William Abikoff, Augmented Teichmüller spaces, Bull. Amer. Math. Soc. 82 (1976), no. 2, 333–334. MR 432919, DOI 10.1090/S0002-9904-1976-14049-9
  • Lars V. Ahlfors, The complex analytic structure of the space of closed Riemann surfaces. , Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 45–66. MR 0124486
  • Lars V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413–429. MR 167618, DOI 10.2307/2373173
  • A. F. Beardon, A primer on Riemann surfaces, London Mathematical Society Lecture Note Series, vol. 78, Cambridge University Press, Cambridge, 1984. MR 808581
  • Lipman Bers, A non-standard integral equation with applications to quasiconformal mappings, Acta Math. 116 (1966), 113–134. MR 192046, DOI 10.1007/BF02392814
  • Lipman Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), no. 1-2, 73–98. MR 477161, DOI 10.1007/BF02545743
  • P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 75–109. MR 262240
  • Ron Donagi, Big Schottky, Invent. Math. 89 (1987), no. 3, 569–599. MR 903385, DOI 10.1007/BF01388986
  • Clifford J. Earle and James Eells Jr., On the differential geometry of Teichmüller spaces, J. Analyse Math. 19 (1967), 35–52. MR 220923, DOI 10.1007/BF02788708
  • H. M. Farkas and I. Kra, Riemann surfaces, 2nd ed., Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York, 1992. MR 1139765, DOI 10.1007/978-1-4612-2034-3
  • Hershel M. Farkas and Harry E. Rauch, Period relations of Schottky type on Riemann surfaces, Ann. of Math. (2) 92 (1970), 434–461. MR 283193, DOI 10.2307/1970627
  • Otto Forster, Lectures on Riemann surfaces, Graduate Texts in Mathematics, vol. 81, Springer-Verlag, New York-Berlin, 1981. Translated from the German by Bruce Gilligan. MR 648106
  • R. Fricke and F. Klein, Vorlesungen über die Theorie der elliptischen Modulfunktionen, B.G. Teubner, 1890-2.
  • 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
  • E. Girondo and G. Gonzáles-Diez, Introduction to Compact Riemann Surfaces and Dessins d’Enfants, vol. 79, London Mathematical Society Student Texts, 2012.
  • J.H. Hubbard and S.C. Koch, An analytic construction of the Deligne-Mumford compactification of the moduli space of curves, to appear.
  • Y. Imayoshi and M. Taniguchi, An introduction to Teichmüller spaces, Springer-Verlag, Tokyo, 1992. Translated and revised from the Japanese by the authors. MR 1215481, DOI 10.1007/978-4-431-68174-8
  • J. Jost, Compact Riemann Surfaces, Springer-Verlag, 1992.
  • J. Kahn and V. Markovic, The good pants homology and a proof of the Ehrenpreis conjecture, Preprint arXiv:1101.1330 (2011).
  • —, Immersing almost geodesic surfaces in a closed hyperbolic three manofold, to appear in Ann. of Math. arXiv:0910.5501.
  • Olli Lehto, Univalent functions and Teichmüller spaces, Graduate Texts in Mathematics, vol. 109, Springer-Verlag, New York, 1987. MR 867407, DOI 10.1007/978-1-4613-8652-0
  • Bernard Maskit, Kleinian groups, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 287, Springer-Verlag, Berlin, 1988. MR 959135
  • Rick Miranda, Algebraic curves and Riemann surfaces, Graduate Studies in Mathematics, vol. 5, American Mathematical Society, Providence, RI, 1995. MR 1326604, DOI 10.1090/gsm/005
  • Subhashis Nag, The complex analytic theory of Teichmüller spaces, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1988. A Wiley-Interscience Publication. MR 927291
  • Raghavan Narasimhan, Compact Riemann surfaces, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 1992. MR 1172116, DOI 10.1007/978-3-0348-8617-8
  • H. E. Rauch, A transcendental view of the space of algebraic Riemann surfaces, Bull. Amer. Math. Soc. 71 (1965), 1–39. MR 213543, DOI 10.1090/S0002-9904-1965-11225-3
  • Bernhard Riemann, Collected papers, Kendrick Press, Heber City, UT, 2004. Translated from the 1892 German edition by Roger Baker, Charles Christenson and Henry Orde. MR 2121437
  • H. L. Royden, Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 369–383. MR 0288254
  • Takahiro Shiota, Characterization of Jacobian varieties in terms of soliton equations, Invent. Math. 83 (1986), no. 2, 333–382. MR 818357, DOI 10.1007/BF01388967
  • Dennis Sullivan, Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains, Ann. of Math. (2) 122 (1985), no. 3, 401–418. MR 819553, DOI 10.2307/1971308
  • Dennis P. Sullivan and William P. Thurston, Extending holomorphic motions, Acta Math. 157 (1986), no. 3-4, 243–257. MR 857674, DOI 10.1007/BF02392594
  • Oswald Teichmüller, Extremale quasikonforme Abbildungen und quadratische Differentiale, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1939 (1940), no. 22, 197 (German). MR 0003242
  • William P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417–431. MR 956596, DOI 10.1090/S0273-0979-1988-15685-6
  • Hermann Weyl, The concept of a Riemann surface, ADIWES International Series in Mathematics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964. Translated from the third German edition by Gerald R. MacLane. MR 0166351
  • Bert van Geemen, Siegel modular forms vanishing on the moduli space of curves, Invent. Math. 78 (1984), no. 2, 329–349. MR 767196, DOI 10.1007/BF01388598
  • Scott A. Wolpert, Thurston’s Riemannian metric for Teichmüller space, J. Differential Geom. 23 (1986), no. 2, 143–174. MR 845703
    •
    Review Information:

    Reviewer: Irwin Kra
    Affiliation: State University of New York at Stony Brook
    Email: irwinkra@gmail.com
    Journal: Bull. Amer. Math. Soc. 49 (2012), 455-463
    DOI: https://doi.org/10.1090/S0273-0979-2012-01375-7
    Published electronically: April 18, 2012
    Review copyright: © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.