@article{RM_1973_28_4_a7,
author = {L. Bers},
title = {Uniformization. {Moduli} and {Kleinian} groups},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
year = {1973},
volume = {28},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/RM_1973_28_4_a7/}
}
L. Bers. Uniformization. Moduli and Kleinian groups. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 28 (1973) no. 4. http://geodesic.mathdoc.fr/item/RM_1973_28_4_a7/
[1] W. Abikoff, “Some remarks on Kleinian groups”, Advances in the theory of Riemann surfaces, Ann. of Math. Stud., 66, 1971, 1–5 | MR
[2] W. Abikoff, “Residual limit sets of Kleinian groups”, Acta Math., 130 (1973), 127–144 | DOI | MR | Zbl
[3] R. D. M. Accola, “Invariant domains for Kleinian groups”, Amer. J. Math., 88 (1966), 329–336 | DOI | MR | Zbl
[4] L. V. Ahlfors, “On quasiconformal mappings”, J. Anal. Math., 3 (1953/54), 1–58 ; V. Alfors, “O kvazikonformnykh otobrazheniyakh”, Prostranstva rimanovykh poverkhnostei i kvazikonformnye otobrazheniya, IL, M., 1961, 104–172 | DOI | MR
[5] L. V. Ahlfors, “The complex analytic structure of the space of closed Riemann surfaces”, Analytic Functions, Princeton University Press, 1960, 349–376 ; L. V. Alfors, “Kompleksno analiticheskaya struktura v prostranstve zamknutykh rimanovykh poverkhnostei”, Prostranstva rimanovykh poverkhnostei i kvazikonformnye otobrazheniya | MR
[6] L. V. Ahlfors, “Some remarks on Teichmuller's space of Riemann surfaces”, Ann. of Math., 74 (1961), 171–191 | DOI | MR | Zbl
[7] L. V. Ahlfors, “Curvature properties of Teichmuller's space”, J. d'Anal., 9 (1961), 161–176 | MR | Zbl
[8] L. V. Ahlfors, “Teichmuller spaces”, Proc. Internat. Congress Math. (1962), Institute Mittag-Leffler, Djursholm, Sweden, 1963, 3–9 | MR
[9] L. V. Ahlfors, “Quasiconformal reflections”, Acta Math., 109 (1963), 291–301 | DOI | MR | Zbl
[10] L. V. Ahlfors, “Finitely generated Kleinian groups”, Amer. J. Math., 86 (1964), 413–429 ; 87 (1965), 759 | DOI | MR | DOI | MR | Zbl
[11] L. V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand, Princeton, 1966 ; L. V. Alfors, Lektsii o kvazikonformnykh otobrazheniyakh, «Mir», M., 1969 | MR | Zbl
[12] L. V. Ahlfors, “Fundamental polyhedrons and limit point sets of Kleinian groups”, Proc. Nat. Acad. Sci., 55 (1966), 251–254 | DOI | MR | Zbl
[13] L. V. Ahlfors, “Eichler integrals and Bers' area theorem”, Mich. Math. J., 15 (1968), 257–263 | DOI | MR | Zbl
[14] L. V. Ahlfors, “The structure of finitely generated Kleinian groups”, Acta Math., 122 (1969), 1–17 | DOI | MR | Zbl
[15] L. V. Ahlfors, L. Bers, “Riemann's mapping theorem for variable metrics”, Ann. of Math., 72 (1960), 385–404 | DOI | MR | Zbl
[16] L. V. Ahlfors, L. Sario, Riemann Surfaces, Princeton University Press, Princeton, N. J., 1960 | MR
[17] L. V. Ahlfors, G. Weill, “A uniqueness theorem for Beltrami equations”, Proc. Amer. Math. Soc., 13 (1962), 975–978 | DOI | MR | Zbl
[18] P. Appel, E. Goursat, Theorie des fonctions algebriques et des leurs integrales, V. 2, Gauthiers-Villars, 1930
[19] W. L. Baily, Jr., “On moduli of Jacobian varieties”, Ann. of Math., 71 (1960), 303–314 | DOI | MR | Zbl
[20] W. L. Baily, Jr., “On the theory of $\Theta$-tfunctions, the moduli of abelian varieties, and the moduli of curves”, Ann. of Math., 75 (1962), 342–381 | DOI | MR | Zbl
[21] L. Bers, “Quasiconformal mappings and Teichmuller's theorem”, Analytic Functions, Princeton University Press, Princeton, 1960, 89–119 ; L. Bers, “Kvazikonformnye otobrazheniya i teorema Teikhmyullera”, Prostranstva rimanovykh poverkhnostei i kvazikonformnye otobrazheniya, IL, M., 1961, 9–50 | MR | Zbl
[22] L. Bers, “Spaces of Riemann surfaces”, Proc. Internat. Congress Math., Edinburgh, 1958, 349–361 ; L. Bers, “Prostranstva rimanovykh poverkhnostei”, Prostranstva rimanovykh poverkhnostei i kvazikonformnye otobrazheniya, IL, M., 1961, 80–90 | MR
[23] L. Bers, “Simultaneous uniformization”, Bull. Amer. Math. Soc., 66 (1960), 94–97 ; L. Bers, “Odnovremennaya uniformizatsiya”, Prostranstva rimanovykh poverkhnostei i kvazikonformnye otobrazheniya, IL, M., 1961 | DOI | MR | Zbl
[24] L. Bers, “Completeness theorems for Poincaré series in one variable”, Proc. Internat. Symp. on Linear Spaces, Jerusalem, 1960, 88–100 | MR
[25] L. Bers, “Uniformization by Beltrami equation”, Comm. Pure Appl. Math., 14 (1961), 215–228 | DOI | MR | Zbl
[26] L. Bers, “Holomorphic differentials as functions of moduli”, Bull. Amer. Math. Soc., 67 (1961), 206–210 | DOI | MR | Zbl
[27] L. Bers, “Correction to: Spaces of Riemann surfaces as bounded domains”, Bull. Amer. Math. Soc., 67 (1961), 465–466 | DOI | MR
[28] L. Bers, “Automorphic forms and general Teichmüller spaces”, Proc. Conf. Complex Analysis (Minneapolis, 1964), Springer, 1965, 109–113 | MR
[29] L. Bers, “On moduli of Riemann surfaces”, Lectures at Forschunginstitut fur Mathematik (Summer 1964), Eidgenossische Technische Hochschule, Zurich, mimeographed
[30] L. Bers, “Automorphic forms and Poincaré series for infinitely generated Fuchsian groups”, Amer. J. Math., 87 (1965), 169–214 | DOI | MR
[31] L. Bers, “A non-standard integral equation with applications to quasiconformal mappings”, Acta Math., 116 (1966), 113–134 | DOI | MR | Zbl
[32] L. Bers, “Inequalities for finitely generated Kleinian groups”, J. Analyse Math., 18 (1967), 23–41 | DOI | MR | Zbl
[33] L. Bers, “On boundaries of Teichmuller spaces and on Kleinian groups, I”, Ann. of Math., 91 (1970), 570–600 | DOI | MR | Zbl
[34] L. Bers, “Spaces of Kleinian groups”, Several Complex Variables, I (Maryland, 1970), Lecture Notes in Math., 155, Springer-Verlag, 1970, 9–34 | MR
[35] L. Bers, “Extremal quasiconformal mappings”, Advances in the Theory of Riemann Surfaces, Ann. of Math. Studies, 66, Princeton, 1971, 27–52 | MR
[36] L. Bers, “Eichler integrals with singularities”, Acta Math., 127 (1971), 11–22 | DOI | MR | Zbl
[37] L. Bers, “Fiber spaces over Teichmüller spaces”, Acta. Math., 130 (1973), 89–126 | DOI | MR | Zbl
[38] L. Bers, L. Ehrenpreis, “Holomorphic convexity of Teichmüller spaces”, Bull. Amer. Math. Soc., 70 (1964), 761–764 | DOI | MR | Zbl
[39] L. Bers, L. Greenberg, “Isomorphisms between Teichmüller spaces”, Advances in the theory of Riemann Surfaces, Ann. of Math. Studies, 66, 1971, 53–79 | MR
[40] A. Beurling, L. V. Ahlfors, “The boundary correspondence for quasiconformal mappings”, Acta Math., 96 (1956), 125–142 | DOI | MR | Zbl
[41] J. Birman, “Automorphisms of the fundamental group of a closed orientable 2-manifold”, Proc. Amer. Math. Soc., 21 (1969), 351–354 | DOI | MR | Zbl
[42] H. Cartan, “Quotent d'un espace analytique par un group $\mathrm{d}$-automorphismes”, Algebraic Geometry and Algebraic Topology, A Symposium in Honor of S. Lefschetz, Princeton University Press, 1957, 90–102 | MR | Zbl
[43] V. Chuckrow, “On Schottky groups with applications to Kleinian groups”, Ann of Math., 88 (1968), 47–61 | DOI | MR | Zbl
[44] H. D. Coldewey, H. Zieschang, “Der Raum der markeirten Reimannschen Flächen”, appendix to: H. Zieschang, E. Vogt, H. D. Coldewey, Flächen, und ebene Diskontinuierliche Gruppen, Lecture Notes in Mathematics, 122, Springer-Verlag, 1970 | MR
[45] C. J. Earle, “The contractability of certain Teichmüller spaces”, Bull. Amer. Math. Soc., 73 (1967), 434–437 | DOI | MR | Zbl
[46] C. J. Earle, “Reduced Teichmüller spaces”, Trans. Amer. Math. Soc., 126 (1967), 54–63 | DOI | MR | Zbl
[47] C. J. Earle, “The Teichmüller spaces for arbitrary Fuchsian groups”, Bull. Amer. Math. Soc., 70 (1964), 699–701 | DOI | MR | Zbl
[48] C. J. Earle, “A reproducing formula for integrable automorphic forms”, Amer. J. Math., 88 (1966), 867–870 | DOI | MR | Zbl
[49] C. J. Earle, “Some remarks on Poincaré series”, Compos. Math., 21 (1969), 167–176 | MR | Zbl
[50] C. J. Earle, “On holomorphic cross-sections in Teichmüller spaces”, Duke Math. J., 33 (1969), 409–416 | DOI | MR
[51] C. J. Earle, J., Jr. Eels, “On the differential geometry of Teichmüller spaces”, J. Analyse Math., 19 (1967), 35–52 | DOI | MR | Zbl
[52] C. J. Earle, J., Jr. Eels, “A fibre bundle description of Teichmüller theory”, J. Diff. Geom., 3 (1969), 19–43 | MR | Zbl
[53] M. Eichler, “Eine Verallgemeinerung der Abelschen Integrale”, Math. Z., 67 (1957), 267–298 | DOI | MR | Zbl
[54] W. Fenchel, J. Nielsen, Discontinuous Groups of Non-euclidean Motions
[55] L. R. Ford, Automorphic Functions, 2nd ed., Chelsea, New York, 1951; L. R. Ford, Avtomorfnye funktsii, ONTI, M., 1936
[56] R. Fricke, F. Klein, Vorlesungen Über die Theorie der Automorphen Funktionen, V. 1, B. G. Teubner, 1926
[57] R. Fricke, F. Klein, Vorlesungen Über die Theorie der Automorphen Funktionen, V. 2, B. G. Teubner, 1926
[58] F. Gardiner, “An analysis of the group operation in universal Teichmüller space”, Trans. of Amer. Math. Soc., 132:2 (1968), 471–486 | DOI | MR | Zbl
[59] J. P. Gilman, Relative modular groups in Teichmüller space, Ph. D. Thesis, Columbia University, 1971
[60] L. Greenberg, “Fundamental polyhedera for Kleinian groups”, Ann. of Math., 84 (1966), 433–441 | DOI | MR | Zbl
[61] P. A. Griffiths, “Complex analytic properties of certain Zariski open sets on algebraic varieties”, Ann. of Math., 94 (1971), 21–51 | DOI | MR | Zbl
[62] A. Grothendieck, “Techniques de construction en geometrie analytique”, Seminaire H. Cartan, Paris, 1960–1961, 7–8
[63] R. S. Hamilton, “Extremal quasiconformal mappings with prescribed boundary values”, Trans. Amer. Math. Soc., 138 (1969), 399–406 | DOI | MR | Zbl
[64] W. J. Harvey, “Cyclic groups of automorphisms of a compact Riemann surface”, Quarterly J. Math., 17 (1966), 86–97 | DOI | MR | Zbl
[65] L. Keen, “Intrinsic moduli on Riemann surfaces”, Ann. of Math., 84 (1966), 404–420 | DOI | MR | Zbl
[66] L. Keen, “On Fricke moduli”, Advances in the theory of Riemann Surfaces, Ann. of Math. Studies, 66, 1971, 205–224 | MR
[67] F. Klein, Gesammelte Matehmatische Abhandlungen, V. 3, Springer, 1923 | Zbl
[68] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker | MR
[69] P. Koebe, “Über die Uniformisierung beliebiger analytischer Kurven”, Goettingener Nachr., 1907, 191–210 ; 633–669 | Zbl | Zbl
[70] P. Koebe, “Über die Uniformisierung algebraischer Kurven”, Math. Ann., 67 (1909), 145–224 ; 69 (1910), 1–81 ; 72 (1912), 437–516 ; 75 (1914), 42–129 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl
[71] P. Koebe, “Über die Uniformisierung beliebiger analytischer Kurven”, J. reine angew. Math., 138 (1910), 192–253 ; 139 (1911), 251–292 | Zbl | Zbl
[72] P. Koebe, “Methoden der $K$ formen abbildung und Uniformisierung”, Intern. Cong. Math., V. 3 (Bologna), 1928, 195–203
[73] I. Kra, “On Teichmüller spaces for finitely generated Fuchsian groups”, Amer. J. Math., 91 (1969), 67–74 | DOI | MR | Zbl
[74] I. Kra, “On cohomology of Kleinian groups”, Ann. of Math., 89 (1969), 533–556 | DOI | MR | Zbl
[75] I. Kra, “On cohomology of Kleinian groups, II”, Ann. of Math., 90 (1969), 576–590 | DOI | MR | Zbl
[76] I. Kra, “Eichler cohomology and the structure of finitely generated Kleinian groups”, Advances in the Theory of Riemann Surfaces, Ann of Math. Studies, 66, 1971, 225–623 | MR
[77] I. Kra, “Cohomology of Kleinian groups, III”, Acta. Math.
[78] S. Kravetz, “On the geometry of Teichmüller spaces and the structure of their modular groups”, Ann. Acad. Sci. Fenn., 278 (1959), 1–35 | MR
[79] S. L. Kruskal, “O teoreme Teikhmyullera otnositelno ekstremalnykh kvazikonformnykh otobrazhenii”, Sibirsk. matem. zh., 8 (1967), 313–332 | MR | Zbl
[80] J. Lehner, Discontinuous groups and automorphic functions, Amer. Math. Soc., 1964 | MR | Zbl
[81] O. Lehto, K. I. Virtanen, Quasikonforme Abbildungen, Springer-Verlag, Berlin, 1965 | MR | Zbl
[82] M. R. Linch, On Metrics in Teichmüller Spaces, Ph. D. Thesis, Columbia University, 1971
[83] C. Machlachlan, “Moduli space is simply connected”, Proc. Amer. Math. Soc.
[84] B. Maskit, “On Klein's combination theorem, I”, Trans. Amer. Math. Soc., 120 (1965), 499–509 | DOI | MR | Zbl
[85] B. Maskit, “On Klein's combination theorem, II”, Trans. Amer. Math. Soc., 131 (1968), 32–39 | DOI | MR | Zbl
[86] B. Maskit, “On boundaries of Teichmuller spaces and on Kleinian groups, II”, Ann. of Math., 91 (1970), 608–638 | DOI | MR
[87] B. Maskit, “On Klein's combination theorem, III”, Advances in the theory of Riemann surfaces, Ann. of Math. Studies, 66, 1971, 297–316 | MR
[88] B. Maskit, “Selfmaps of Kleinian groups”, Amer. J. Math.
[89] B. Maskit, “On Poincaré's theorem for fundamental polygons”, Advances in Math., 1 (1971), 219–230 | DOI | MR
[90] A. Marden, “On homotopic mappings of Riemann surfaces”, Ann. of Math., 90 (1969), 1–8 | DOI | MR | Zbl
[91] A. Marden, “An inequality for Kleinian groups”, Advances in the theory of Riemann surfaces, Ann. of Math. Studies, 66, 1971, 295–296 | MR
[92] C. B. Morrey, “On the solutions of quasilinear elliptic partial differential equations”, Trans. Amer. Math. Soc., 43 (1938), 126–166 | DOI | MR
[93] P. J. Myrberg, “Die Kapazität der singulären Menge der linearen gruppen”, Ann. Acad. Sci. Fenn., 10 (1941), 1–19 | MR | Zbl
[94] Z. Nehari, “Schwarzian derivatives and schlicht functions”, Bull. Amer. Math. Soc., 55 (1949), 545–551 | DOI | MR | Zbl
[95] R. Nevanlinna, Uniformisierung, Springer, Berlin, 1953 ; R. Nevanlinna, Uniformizatsiya, M. | MR | MR
[96] Olsen, A. Bruce, On higher order Weierstrass points, Ph. D. Thesis, Columbia University, 1971
[97] H. Petersson, “Über eine Metrisierung der automorphen Formen und die Theorie der Poincareschen Reihen”, Math. Ann., 117 (1940), 453–537 | DOI | MR
[98] H. Petersson, “Über Weierstrass Punkte und die expliziten Darstellungen der automorphen Formen von reeller Dimension”, Math. Z., 52 (1949), 32–59 | DOI | MR | Zbl
[99] A. Pfluger, Theorie der Riemannschen Flächen, Springer-Verlag, Berlin, 1957 | MR | Zbl
[100] H. Poincaré, Oevres, Vol. 2, Gauthiers - Villar, 1916
[101] H. Poincaré, “Sur l'uniformisation des fonctions analytiques”, Acta. Math., 31 (1907), 1–63 | DOI | MR
[102] H. E. Rauch, “Weierstrass points, branch points, and the moduli of Riemann surfaces”, Comm. Pure Appl. Math., 12 (1959), 543–560 | DOI | MR
[103] H. E. Rauch, “A transcendential view of the space of algebraic Riemann surfaces”, Bull. Amer. Math. Soc., 71 (1965), 1–39 | DOI | MR | Zbl
[104] H. L. Royden, “Automorphisms and isometries of Teichmüller spaces”, Advances in the Theory of Riemann Surfaces, Princeton University Press, Princeton, N.J., 1971, 369–383 | MR
[105] C. L. Siegel, Topics in Complex Function Theory, V. 2, Wiley- Interscience, 1971 | Zbl
[106] G. Springer, Introduction to Riemann Surfaces, Addison - Wisley, 1957 ; Springer, Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1960 | MR | Zbl
[107] O. Teichmüller, “Extremale quasikonforme Abbildungen und quadratische Differentiale”, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl., 22 (1939) | MR
[108] O. Teichmüller, “Bestimmung der extremalen quasikonformen Abbildung bei geschlossenen orientierten Riemannschen Flachen”, Preussische Acad. Ber., 4 (1943) | MR | Zbl
[109] O. Teichmüller, “Veranderlich Riemannsche Flachen”, Deutsche Math., 9 (1944), 344–359 | MR
[110] A. Weil, “Sur les modules des surfaces de Riemann”, Seminare Bourbaki, 1958
[111] H. Weyl, Die Idee der Riemannschen Flache, Teubner, Leipzig, 1955 | MR | Zbl