RUS  ENG
Full version
JOURNALS // Uspekhi Matematicheskikh Nauk

Uspekhi Mat. Nauk, 2013, Volume 68, Issue 3(411), Pages 39–110 (Mi rm9517)

Classical and quantum Teichmüller spaces
A. Yu. Vasiliev, A. G. Sergeev

References

1. W. Abikoff, “Augmented Teichmüller spaces”, Bull. Amer. Math. Soc., 82:2 (1976), 333–334  crossref  mathscinet  zmath
2. W. Abikoff, “Degenerating families of Riemann surfaces”, Ann. of Math. (2), 105:1 (1977), 29–44  crossref  mathscinet  zmath
3. W. Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Math., 820, Springer, Berlin, 1980, vii+144 pp.  mathscinet  mathscinet  zmath  zmath
4. W. Abikoff, “Oswald Teichmüller”, Math. Intelligencer, 8:3 (1986), 8–16, 33  crossref  mathscinet  zmath
5. W. Abikoff, C. Corillon, J. Gilman, I. Kra, T. Weinstein, “Remembering Lipman Bers”, Notices Amer. Math. Soc., 42:1 (1995), 8–25  mathscinet  zmath
6. L. Ahlfors, “Zur Theorie der Überlagerungsflächen”, Acta Math., 65:1 (1935), 157–194  crossref  mathscinet  zmath
7. L. V. Ahlfors, “On quasiconformal mappings”, J. Analyse Math., 3:1 (1953/1954), 1–58  crossref  mathscinet  zmath; 104–172
8. L. Ahlfors, “Curvature properties of Teichmüller's space”, J. Anal. Math., 9:1 (1961/1962), 161–176  crossref  mathscinet  zmath
9. L. V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand Math. Stud., 10, D. Van Nostrand Co., Inc., Toronto–New York–London, 1966, v+146 pp.  mathscinet  mathscinet  zmath  zmath
10. L. Ahlfors, Conformal invariants: topics in geometric function theory, McGraw-Hill Ser. in Higher Math., McGraw-Hill Book Co., New York–Düsseldorf–Johannesburg, 1973, ix+157 pp.  mathscinet  zmath
11. L. Alfors, L. Bers, Prostranstva rimanovykh poverkhnostei i kvazikonformnye otobrazheniya, IL, M., 1961, 177 pp.  mathscinet
12. L. V. Ahlfors, A. Beurling, “Invariants conformes et problèmes extrémaux”, Comptes Rendus du Dixième Congrès des Mathematiciens Scandinaves 1946, Jul. Gjellerups Forlag, Copenhagen, 1947, 341–351  mathscinet  zmath
13. P. P. Belinskii, Obschie svoistva kvazikonformnykh otobrazhenii, Nauka, Novosibirsk, 1974, 98 pp.  mathscinet  zmath
14. F. A. Berezin, Metod vtorichnogo kvantovaniya, 2-e izd., Nauka, M., 1986, 320 pp.  mathscinet  zmath
15. L. Bers, “Isolated singularities of minimal surfaces”, Ann. of Math. (2), 53:2 (1951), 364–386  crossref  mathscinet  zmath
16. L. Bers, “Quasiconformal mappings and Teichmüller's theorem”, Analytic functions, Princeton Univ. Press, Princeton, NJ, 1960, 89–119  mathscinet  zmath; 9–50
17. L. Bers, “Universal Teichmüller space”, Analytic methods in mathematical physics (Indiana Univ., Bloomington, IN, 1968), Gordon and Breach, New York, 1970, 65–83  mathscinet  zmath
18. L. Bers, “On boundaries of Teichmüller spaces and on Kleinian groups. I”, Ann. of Math. (2), 91:3 (1970), 570–600  crossref  mathscinet  zmath
19. L. Bers, “An extremal problem for quasiconformal mappings and a theorem by Thurston”, Acta Math., 141:1-2 (1978), 73–98  crossref  mathscinet  zmath
20. L. Bers, I. Kra (eds.), A crash course on Kleinian groups, Lectures given at a special session at the Annual Winter Meeting of the American Mathematical Society (San Francisco, CA, January 1974), Lecture Notes in Math., 400, Springer-Verlag, Berlin–New York, 1974, v+130 pp.  crossref  mathscinet  zmath
21. R. Bowen, “Hausdorff dimension of quasi-circles”, Inst. Hautes Études Sci. Publ. Math., 50:1 (1979), 11–25  crossref  mathscinet  zmath
22. M. J. Bowick, S. G. Rajeev, “The holomorphic geometry of closed bosonic string theory and $\operatorname{Diff}S^1/S^1$”, Nuclear Phys. B, 293:2 (1987), 348–384  crossref  mathscinet  adsnasa
23. M. R. Chowdhury, “Landau and Teichmüller”, Math. Intelligencer, 17:2 (1995), 12–14  crossref  mathscinet  zmath
24. A. Connes, Géométrie non commutative, InterEditions, Paris, 1990, 240 pp.  mathscinet  zmath
25. P. Deligne, D. Mumford, “The irreducibility of the space of curves of given genus”, Inst. Hautes Études Sci. Publ. Math., 36:1 (1969), 75–109  crossref  mathscinet  zmath
26. V. N. Dubinin, “Symmetrization in the geometric theory of functions of a complex variable”, Russian Math. Surveys, 49:1 (1994), 1–79  mathnet  crossref  mathscinet  zmath  adsnasa
27. C. J. Earle, “On the Carathéodory metric in Teichmüller spaces”, Discontinuous groups and Riemann surfaces (Univ. Maryland, College Park, MD, 1973), Ann. of Math. Studies, 79, Princeton Univ. Press, Princeton, NJ, 1974, 99–103  mathscinet  zmath
28. L. D. Faddeev, V. N. Popov, “Feynman diagrams for the Yang–Mills field”, Phys. Lett. B, 25:1 (1967), 29–30  crossref  adsnasa
29. A. Fathi, F. Laudenbach, V. Poénaru (eds.), Travaux de Thurston sur les surfaces, Séminaire Orsay, Astérisque, 66-67, Soc. Math. France, Paris, 1979, 284 pp.  mathscinet  zmath
30. A. Fletcher, V. Markovic, Quasiconformal maps and Teichmüller theory, Oxf. Grad. Texts Math., 11, Oxford Univ. Press, Oxford, 2007, viii+189 pp.  mathscinet  zmath
31. V. V. Fock, L. O. Chekhov, “A quantum Teichmüller space”, Theoret. and Math. Phys., 120:3 (1999), 1245–1259  mathnet  crossref  crossref  mathscinet  zmath
32. F. P. Gardiner, Teichmüller theory and quadratic differentials, Pure Appl. Math. (N. Y.), A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1987, xviii+236 pp.  mathscinet  zmath
33. F. P. Gardiner, N. Lakic, Quasiconformal Teichmüller theory, Math. Surveys Monogr., 76, Amer. Math. Soc., Providence, RI, 2000, xx+372 pp.  mathscinet  zmath
34. F. P. Gardiner, D. P. Sullivan, “Symmetric structures on a closed curve”, Amer. J. Math., 114:4 (1992), 683–736  crossref  mathscinet  zmath
35. R. Goodman, N. R. Wallach, “Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle”, J. Reine Angew. Math., 347 (1984), 69–133  crossref  mathscinet  zmath
36. T. Gotô, “Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary condition of dual resonance model”, Progr. Theoret. Phys., 46:5 (1971), 1560–1569  crossref  mathscinet  zmath  adsnasa
37. J. M. Gracia-Bondía, J. C. Várilly, H. Figueroa, Elements of noncommutative geometry, Birkhäuser Adv. Texts Basler Lehrbücher, Birkhäuser Boston, Inc., Boston, MA, 2001, xviii+685 pp.  mathscinet  zmath
38. H. Grötzsch, “Über einige Extremalprobleme der konformen Abbildung. I, II”, Berichte Leipzig, 80 (1928), 367–376, 497–502  zmath
39. R. Guo, “A survey of quantum Teichmüller space and Kashaev algebra”, Handbook of Teichmüller space, v. IV, ed. A. Papadopoulos, Eur. Math. Soc., Zürich, 27 pp. (to appear); 2011, arXiv: 1107.5069
40. R. Guo, X. Liu, “Quantum Teichmüller space and Kashaev algebra”, Algebr. Geom. Topol., 9:3 (2009), 1791–1824  crossref  mathscinet  zmath
41. R. A. Hidalgo, A. Vasil'ev, “Noded Teichmüller spaces”, J. Anal. Math., 99:1 (2006), 89–107  crossref  mathscinet  zmath
42. E. D'Hoker, D. H. Phong, “Multiloop amplitudes for the bosonic Polyakov string”, Nuclear Phys. B, 269:1 (1986), 205–234  crossref  mathscinet  adsnasa
43. J. H. Hubbard (ed.), Teichmüller theory and applications to geometry, topology, and dynamics, v. 1, Teichmüller theory, Matrix Editions, Ithaca, NY, 2006, xx+459 pp.  mathscinet  zmath
44. A. Hurwitz, “Ueber Riemann'sche Flächen mit gegebenen Verzweigungspunkten”, Math. Ann., 39 (1891), 1–61  crossref  mathscinet  zmath; Reprinted in: A. Hurwitz, Mathematische Werke. Bd. I, Funktionentheorie, Birkhäuser, Basel, 1932, 321–381  crossref  mathscinet  zmath
45. Y. Imayoshi, M. Taniguchi, An introduction to Teichmüller spaces, Springer-Verlag, Tokyo, 1992, xiv+279 pp.  mathscinet  zmath
46. R. J. Milgram, R. C. Penner, “Riemann's moduli space and the symmetric groups”, Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991), Contemp. Math., 150, Amer. Math. Soc., Providence, RI, 1993, 247–290  crossref  mathscinet  zmath
47. J. A. Jenkins, “On the existence of certain general extremal metrics”, Ann. of Math. (2), 66:3 (1957), 440–453  crossref  mathscinet  zmath
48. J. A. Jenkins, Univalent functions and conformal mapping, Ergeb. Math. Grenzgeb. N. F., 18, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1958, vi+169 pp.  mathscinet  zmath
49. J. Jost, Bosonic strings: a mathematical treatment, AMS/IP Stud. Adv. Math., 21, Amer. Math. Soc., Providence, RI; International Press, Somerville, MA, 2001, xii+95 pp.  mathscinet  zmath
50. V. G. Kac, A. K. Raina, Bombay lectures on highest weight representations of infinite-dimensional Lie algebras, Adv. Ser. Math. Phys., 2, World Scientific Publishing Co., Inc., Teaneck, NJ, 1987, xii+145 pp.  mathscinet  zmath
51. R. M. Kashaev, “Quantization of Teichmüller spaces and the quantum dilogarithm”, Lett. Math. Phys., 43:2 (1998), 105–115  crossref  mathscinet  zmath
52. S. P. Kerckhoff, “The asymptotic geometry of Teichmüller space”, Topology, 19:1 (1980), 23–41  crossref  mathscinet  zmath
53. S. P. Kerckhoff, W. P. Thurston, “Non-continuity of the action of the modular group at Bers' boundary of Teichmüller space”, Invent. Math., 100:1 (1990), 25–47  crossref  mathscinet  zmath  adsnasa
54. A. A. Kirillov, D. V. Yur'ev, “Kähler geometry of the infinite-dimensional homogeneous space $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$”, Funct. Anal. Appl., 21:4 (1987), 284–294  mathnet  crossref  mathscinet  zmath
55. F. Klein, Ueber Riemann's Theorie der algebraischen Funktionen und ihrer Integrale, B. G. Teubner, Leipzig, 1882, 82 pp.  mathscinet  zmath; Reprinted in: F. Klein, Gesammelte mathematische Abhandlungen, v. 3, Springer, Berlin, 1923, 499–573  mathscinet  zmath
56. I. Kra, “The Carathéodory metric on Abelian Teichmüller disks”, J. Anal. Math., 40:1 (1981), 129–143  crossref  mathscinet  zmath
57. W. Kraus, “Über den Zusammenhang einiger Charakteristiken eines einfach zusammenhängenden Bereiches mit der Kreisabbildung”, Mitt. Math. Semin. Univ. Giessen, 21 (1932), 1–28  zmath
58. S. L. Krushkal, Quasiconformal mappings and Riemann surfaces, A Halsted Press Book. Scripta Series in Mathematics, V. H. Winston & Sons, Washington, DC; John Wiley & Sons, New York–Toronto–London, 1979, xii+319 pp.  mathscinet  mathscinet  zmath  zmath
59. C. L. Krushkal, “Invariantnye metriki na prostranstvakh Teikhmyullera”, Sib. matem. zhurn., 22:2 (1981), 209–212  mathnet  mathscinet  zmath
60. S. L. Krushkal, “Invariant metrics on Teichmüller spaces and quasiconformal extendability of analytic functions”, Ann. Acad. Sci. Fenn. Ser. A I Math., 10 (1985), 299–303  crossref  mathscinet  zmath
61. S. L. Krushkal, “Hyperbolic metrics on finite-dimensional Teichmüller spaces”, Ann. Acad. Sci. Fenn. Ser. A I Math., 15:1 (1990), 125–132  crossref  mathscinet  zmath
62. S. L. Krushkal, R. Kühnau, Quasikonforme Abbildungen – neue Methoden und Anwendungen, Teubner-Texte Math., 54, BSB B. G. Teubner, Leipzig, 1983, 169 pp.  mathscinet  mathscinet  zmath  zmath
63. G. V. Kuz'mina, “Moduli of families of curves and quadratic differentials”, Proc. Steklov Inst. Math., 139 (1982), 1–231  mathnet  mathscinet  mathscinet  zmath  zmath
64. M. A. Lavrentieff, “Sur une critère differentiel des transformations homeomorphes des domains à trois dimensions”, Dokl. AN SSSR, 20 (1938), 241–242  zmath
65. M. A. Lavrentieff, “Sur une classe de transformations quasi-conformes et sur les sillages gazeux”, Dokl. AN SSSR, 20 (1938), 343–345  zmath
66. O. Lehto, Univalent functions and Teichmüller spaces, Grad. Texts in Math., 109, Springer-Verlag, New York, 1987, xii+257 pp.  crossref  mathscinet  zmath
67. O. Lehto, K. I. Virtanen, Quasiconformal mappings in the plane, Grundlehren Math. Wiss., 126, 2nd ed., Springer-Verlag, New York–Heidelberg, 1973, viii+258 pp.  mathscinet  zmath
68. Li-Xing Liu, “Invariant metrics in infinite-dimensional Teichmüller space”, Complex Variables Theory Appl., 25:4 (1994), 337–349  crossref  mathscinet  zmath
69. H. Masur, “On a class of geodesics in Teichmüller space”, Ann. of Math. (2), 102:2 (1975), 205–221  crossref  mathscinet  zmath
70. S. Nag, “Non-geodesic disks embedded in Teichmüller space”, Amer. J. Math., 104:2 (1982), 399–408  crossref  mathscinet  zmath
71. S. Nag, The complex analytic theory of Teichmüller spaces, Canad. Math. Soc. Ser. Monogr. Adv. Texts, A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1988, xiv+427 pp.  mathscinet  zmath
72. S. Nag, “A period mapping in universal Teichmüller space”, Bull. Amer. Math. Soc. (N.S.), 26:2 (1992), 280–287  crossref  mathscinet  zmath
73. S. Nag, D. Sullivan, “Teichmüller theory and the universal period mapping via quantum calculus and the $H^{1/2}$ space on the circle”, Osaka J. Math., 32:1 (1995), 1–34  mathscinet  zmath
74. S. Nag, A. Verjovsky, “$\operatorname{Diff}(S^1)$ and the Teichmüller spaces”, Comm. Math. Phys., 130:1 (1990), 123–138  crossref  mathscinet  zmath  adsnasa
75. Y. Nambu, Duality and hydrodynamics, Lectures at the Copenhagen summer symposium, 1970
76. Z. Nehari, “Schwarzian derivatives and schlicht functions”, Bull. Amer. Math. Soc., 55:6 (1949), 545–551  crossref  mathscinet  zmath
77. C. Neumann, Vorlesungen über Riemann's Theorie der Abel'schen Integrale, B. G. Teubner, Leipzig, 1865; 2nd ed., 1884, 472 pp.  zmath
78. R. Nevanlinna, Uniformisierung, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, LXIV, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1953, x+391 pp.  mathscinet  zmath
79. J. Nielsen, “Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen”, Acta Math., 50:1 (1927), 189–358  crossref  mathscinet  zmath
80. E. Noether, “Invariante Variationsprobleme”, Gött. Nachr., 1918 (1918), 235–257  zmath  adsnasa
81. J. J. O'Connor, E. F. Robertson, Paul Julius Oswald Teichmüller, MacTutor History of Mathematics archive, Univ. of St. Andrews, 2009 http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Teichmuller.html
82. J. J. O'Connor, E. F. Robertson, Lipman Bers, MacTutor History of Mathematics archive, Univ. of St. Andrews, 2002 http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Bers.html
83. M. Ohtsuka, Dirichlet problem, extremal length, and prime ends, Van Nostrand Reinhold Math. Ser., Van Nostrand Reinhold Co., New York, 1970, 326 pp.  zmath
84. A. Papadopoulos (ed.), Handbook of Teichmüller theory, v. I, IRMA Lect. Math. Theor. Phys., 11, Eur. Math. Soc. (EMS), Zürich, 2007, viii+794 pp.  crossref  mathscinet  zmath; v. II, IRMA Lect. Math. Theor. Phys., 13, 2009, x+874 pp.  crossref  mathscinet  zmath; v. III, IRMA Lect. Math. Theor. Phys., 17, 2012, viii+366 pp.  crossref  mathscinet  zmath; (to appear)
85. O. Pekonen, “Universal Teichmüller space in geometry and physics”, J. Geom. Phys., 15:3 (1995), 227–251  crossref  mathscinet  zmath  adsnasa
86. H. Poincaré, “Sur les fonctions fuchsiennes”, C. R. Acad. Sci. Paris, 92 (1881), 333–335; Reprinted in: {ØE}uvres, v. II, Gauthier-Villars, Paris, 1916, 1–4  mathscinet  zmath
87. E. A. Poletskij, B. V. Shabat, “Invariant metrics”, Several complex variables. III. Geometric function theory, Encycl. Math. Sci., 9, Kluwer, Dordrecht, 1989, 63–111  mathnet  mathscinet  zmath
88. A. M. Polyakov, “Quantum geometry of bosonic strings”, Phys. Lett. B, 103:3 (1981), 207–210  crossref  mathscinet  adsnasa
89. S. Power, Hankel operators on Hilbert space, Res. Notes in Math., 64, Pitman (Advanced Publishing Program), Boston, MA–London, 1982, vii+87 pp.  mathscinet  zmath
90. A. Pressley, G. Segal, Loop groups, Oxford Math. Monogr., 2nd rev. ed., Oxford Univ. Press, New York, 1988, viii+318 pp.  mathscinet  zmath  zmath
91. T. Radó, “Über den Begriff der Riemannschen Fläche”, Acta Litt. Sci. Szeged, 2 (1925), 101–121  zmath
92. B. Riemann, Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Größe, Inauguraldissertation, Göttingen, 1851; Reprinted in: Gesammelte mathematische Werke und wissenschaftlicher Nachlass, 2nd ed., B. G. Teubner, Leipzig, 1902, 3–48  mathscinet  zmath
93. B. Riemann, “Theorie der Abel'schen Functionen”, J. Reine Angew. Math., 54 (1857), 101–155  crossref  zmath
94. H. L. Royden, “Automorphisms and isometries of Teichmüller space”, Advances in the theory of Riemann surfaces (Stony Brook, NY, 1969), Ann. of Math. Stud., 66, Princeton Univ. Press, Princeton, NJ, 1971, 369–383  mathscinet  zmath
95. N. Schappacher, E. Scholz (eds.), “Oswald Teichmüller – Leben und Werk”, Jahresber. Deutsch. Math.-Verein., 94:1 (1992), 1–39  mathscinet  zmath
96. G. Segal, “Unitary representations of some infinite dimensional groups”, Comm. Math. Phys., 80:3 (1981), 301–342  crossref  mathscinet  zmath  adsnasa
97. A. Sergeev, Kähler geometry of loop spaces, MSJ Memoirs, 23, Math. Soc. Japan, Tokyo, 2010, xvi+212 pp.  mathnet  crossref  mathscinet  zmath
98. A. Sergeev, “The group of quasisymmetric homeomorphisms of the circle and quantization of the universal Teichmüller space”, SIGMA Symmetry Integrability Geom. Methods Appl., 5 (2009), paper 015, 20 pp.  mathnet  crossref  mathscinet  zmath
99. A. Sergeev, “Quantization of universal Teichmüller space”, Geometry and quantization, Trav. Math., 19, Univ. Luxembourg, Luxembourg, 2011, 7–26  mathscinet  zmath
100. D. Shale, “Linear symmetries of free boson field”, Trans. Amer. Math. Soc., 103:1 (1962), 149–167  crossref  mathscinet  zmath
101. H. Shiga, H. Tanigawa, “Grunsky's inequality and its applications to Teichmüller spaces”, Kodai Math. J., 16:3 (1993), 361–378  crossref  mathscinet  zmath
102. A. Yu. Solynin, “Moduli and extremal metric problems”, St. Petersburg Math. J., 11:1 (2000), 1–65  mathnet  mathscinet  zmath
103. K. Strebel, Quadratic differentials, Ergeb. Math. Grenzgeb. (3), 5, Springer-Verlag, Berlin, 1984, xii+184 pp.  mathscinet  zmath
104. L. A. Takhtajan, Lee-Peng Teo, Weil–Petersson metric on the universal Teichmüller space, Mem. Amer. Math. Soc., 183, no. 861, Amer. Math. Soc., Providence, RI, 2006, viii+119 pp.  mathscinet  zmath
105. P. M. Tamrazov, “Odna teorema ob integralakh po krivym ekstremalnoi dliny”, Dokl. AN Ukr. SSR, 1 (1966), 51–54  mathscinet  zmath
106. O. Teichmüller, “Untersuchungen über konforme und quasikonforme Abbildung”, Deutsche Math., 3 (1938), 621–678  zmath
107. O. Teichmüller, “Ungleichungen zwischen den Koeffizienten schlichter Funktionen”, Sitzungsber. Preuß. Acad. Wiss. Phys.-Math. Kl., 1938, 363–375  zmath
108. O. Teichmüller, “Extremale quasikonforme Abbildungen und quadratische Differentiale”, Abh. Preuß. Akad. Wiss. Math.-Nat. Kl., 22 (1939), 197 pp.  mathscinet  zmath
109. O. Teichmüller, “Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen”, Abh. Preuß. Akad. Wiss. Math.-Nat. Kl., 4 (1943), 42 pp.  mathscinet  zmath
110. O. Teichmüller, “Veränderliche Riemannsche Flächen”, Deutsche Math., 7 (1944), 344–359  mathscinet  zmath
111. O. Teichmüller, Gesammelte Abhandlungen, eds. L. V. Ahlfors, F. W. Gehring, Springer-Verlag, Berlin–New York, 1982, viii+751 pp.  mathscinet  zmath
112. W. P. Thurston, “On the geometry and dynamics of diffeomorphisms of surfaces”, Bull. Amer. Math. Soc., 19:2 (1988), 417–431  crossref  mathscinet  zmath
113. A. J. Tromba, Teichmüller theory in Riemannian geometry, Lectures Math. ETH Zurich, Birkhäuser Verlag, Basel, 1992, 220 pp.  crossref  mathscinet  zmath
114. A. Yu. Vasil'ev, “Harmonic properties of the module of a family of curves and invariant metrics in Teichmüller space”, Dokl. Math., 51:2 (1995), 237–238  mathnet  mathscinet  zmath
115. A. Yu. Vasil'ev, “Homotopy of curves and mappings and the Teichmüller metric”, Math. Notes, 59:6 (1996), 668–671  mathnet  crossref  crossref  mathscinet  zmath
116. A. Yu. Vasil'ev, “Moduli of families of curves and invariant metrics on Teichmüller space”, Siberian Math. J., 37:5 (1996), 868–875  mathnet  crossref  mathscinet  zmath
117. A. Yu. Vasil'ev, “Invariant metrics and harmonic functionals on the Teichmüller space”, St. Petersburg Math. J., 9:1 (1998), 33–48  mathnet  mathscinet  zmath
118. A. Vasiliev, Moduli of families of curves for conformal and quasiconformal mappings, Lecture Notes in Math., 1788, Springer-Verlag, Berlin, 2002, x+211 pp.  crossref  mathscinet  zmath
119. K. Weierstrass, “Definition analytischer functionen einer Veränderlichen vermittelst algebraischer Differentialgleichungen”, 1842, Mathematische Werke. I. Abhandlungen 1, Mayer & Müller, Berlin, 1894, 75–84  mathscinet  zmath
120. A. Weil, “Modules des surfaces de Riemann”, Séminaire Bourbaki, 10e année: 1957/1958, textes des conférences, exposés 152 à 168, Secrétariat mathématique, Paris, 1958, exp. 168, 7 pp.  mathscinet  zmath
121. H. Weyl, Die Idee der Riemannschen Fläche, B. G. Teubner, Leipzig, 1913, x+169 pp.  zmath
122. S. A. Wolpert, “The topology and geometry of the moduli space of Riemann surfaces”, Workshop Bonn 1984, Lecture Notes in Math., 1111, Springer, Berlin, 1985, 431–451  crossref  mathscinet  zmath
123. S. Wolpert, “On the Weil–Petersson geometry of the moduli space of curves”, Amer. J. Math., 107:4 (1985), 969–997  crossref  mathscinet  zmath
124. S. A. Wolpert, “Thurston's Riemannian metric for Teichmüller space”, J. Differential Geom., 23:2 (1986), 143–174  mathscinet  zmath
125. S. Wolpert, “Chern forms and the Riemann tensor for the moduli space of curves”, Invent. Math., 85:1 (1986), 119–145  crossref  mathscinet  zmath  adsnasa
126. N. M. J. Woodhouse, Geometric quantization, 2nd ed., Oxford Math. Monogr., Oxford Univ. Press, New York, 1992, xii+307 pp.  mathscinet  zmath
127. P. G. Zograf, L. A. Takhtadzhyan, “On Liouville's equation, accessory parameters, and the geometry of Teichmüller space for Riemann surfaces of genus 0”, Math. USSR-Sb., 60:1 (1988), 143–161  mathnet  crossref  mathscinet  zmath
128. P. G. Zograf, L. A. Takhtadzhyan, “On uniformization of Riemann surfaces and the Weil–Petersson metric on Teichmüller and Schottky spaces”, Math. USSR-Sb., 60:2 (1988), 297–313  mathnet  crossref  mathscinet  zmath


© Steklov Math. Inst. of RAS, 2026