Book Review
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2952711
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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
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
References
- W. Abikoff, Augmented Teichmüller spaces, Bull. Amer. Math. Soc. 82 (1976), 333–334. MR 0432919 (55:5898)
- L.V. Ahlfors, The complex analytic stucture of the space of closed Riemann surfaces, Analytic Functions, Princeton University Press, 1960, pp. 45–66. MR 0124486 (23:A1798)
- —, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413–429 and 87 (1965), 759. MR 0167618 (29:4890)
- A. Beardon, A Primer on Riemann Surfaces, London Mathematical Society Lecture Notes, 78, Cambridge University Press, Cambridge, 2011. MR 0808581 (87h:30090)
- L. Bers, A nonstandard integral equation with applications to quasiconformal mappings, Acta Math. 116 (1966), 113–134. MR 0192046 (33:273)
- —, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), 73–98. MR 0477161 (57:16704)
- P. Deligne and D. Mumford, The irreducibility of the space of curves of a given genus, Publ. Math. I.H.E.S. 36 (1969), 75–110. MR 0262240 (41:6850)
- R. Donagi, Big Schottky, Invent. Math. 89 (1987), 569–599. MR 903385 (88j:14052)
- C.J. Earle and Jr. J. Eells, On the differential geometry of Teichmüller spaces, J. Analyse Math. 19 (1967), 35–52. MR 0220923 (36:3975)
- H.M. Farkas and I. Kra, Riemann Surfaces (second edition), Graduate Texts in Mathematics, vol. 71, Springer-Verlag, 1992. MR 1139765 (93a:30047)
- H.M. Farkas and H.E. Rauch, Period relations of Schottky type on Riemann surfaces, Ann. Math. (1970), 434–461. MR 0283193 (44:426)
- O. Forster, Lectures on Riemann Surfaces, Graduate Texts in Mathematics, vol. 81, Springer-Verlag, 1981. MR 648106 (83d:30046)
- R. Fricke and F. Klein, Vorlesungen über die Theorie der elliptischen Modulfunktionen, B.G. Teubner, 1890-2.
- F.P. Gardiner, Teichmüller Theory and Quadratic Differentials, Wiley-Interscience, 1987. MR 903027 (88m:32044)
- 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 Theory, Springer-Verlag, 1992. MR 1215481 (94b:32031)
- 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.
- O. Lehto, Univalent Functions and Teichmüller Spaces, Graduate Texts in Mathematics, vol. 109, Springer-Verlag, 1987. MR 867407 (88f:30073)
- B. Maskit, Kleinian Groups, Grundlehren der Mathematischen Wissenschaften, vol. 287, Springer-Verlag, 1988. MR 959135 (90a:30132)
- R. Miranda, Algebraic Curves and Riemann Surfaces, Graduate Studies in Mathematics, vol. 5, American Mathematical Society, 1995. MR 1326604 (96f:14029)
- S. Nag, The Complex Analytic Theory of Teichmüller Space, Wiley-Interscience, 1988. MR 927291 (89f:32040)
- R. Narasimhan, Compact Riemann Surfaces, Lectures in Mathematics, ETH Zurich, Birkhäuser Verlag, 1992. MR 1172116 (93j:30049)
- H.E. Rauch, A transcendental view of the space of algebraic Riemann surfaces, Bull. Amer. Math. Soc. 71 (1965), 1–39. MR 0213543 (35:4403)
- B. Riemann, Collected Papers, Kendrick Press, 2004 (translated by R. Basker and C. Christenson and H. Orde). MR 2121437 (2005m:01028)
- H.L. Royden, Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces, Ann. of Math. Stud. 66, Princeton University Press, 1971, pp. 369–383. MR 0288254 (44:5452)
- T. Shiota, Characterization of Jacobian varieties in terms of soliton equations, Invent. Math. 83 (1986), 333–382. MR 818357 (87j:14047)
- D. Sullivan, Quasiconformal homeomorphisms and dynamics I, Solution of the Fatou-Julia problem on wandering domains, Ann. of Math. 122 (1985), 401–418. MR 819553 (87i:58103)
- D. Sullivan and W.P. Thurston, Extending holomorphic motions, Acta Math. 157 (1986), 243–257. MR 857674 (88i:30033)
- O. Teichmüller, Extremale quasikonforme Abbildungen und quadratische differentiale, Abh. Preuss. Akad. Wiss. 22 (1940), 1–197. MR 0003242 (2:187a)
- W.P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988), 417–431. MR 956596 (89k:57023)
- H. Weyl (translated by G.R. MacLane), The Concept of a Riemann Surface, Addison-Wesley, 1955. MR 0166351 (29:3628)
- B. van Geemen, Siegel modular forms vanishing on the moduli space of curves, Invent. Math. 78 (1984), 329–349. MR 767196 (86d:14040)
- S. Wolpert, Thurston’s metric for Teichmüller spaces, J. Differential Geom. 23 (1986), 143–174. MR 845703 (88c:32035)
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.