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On a purely ”Riemannian” proof of the structure and dimension of the unramified moduli space of a compact Riemann surface. (English) Zbl 0518.32015

32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
30F10 Compact Riemann surfaces and uniformization
58D17 Manifolds of metrics (especially Riemannian)
35J99 Elliptic equations and elliptic systems
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
32G13 Complex-analytic moduli problems
14H45 Special algebraic curves and curves of low genus
Full Text: DOI EuDML
[1] Abraham, R., Marsden, J.: Foundations of mechanics. New York: Benjamin 1978 · Zbl 0393.70001
[2] Ahlfors, L.V.: On quasiconformal mappings. J. Analyse Math.4, 1-58 (1954) · Zbl 0065.30502 · doi:10.1007/BF02787715
[3] Ahlfors, L.V.: Some remarks on Teichmüller’s space of Riemann surfaces. Ann. Math.74, 1 (1961) · Zbl 0146.30602 · doi:10.2307/1970309
[4] Ahlfors, L.V.: The complex analytic structure of the space of closed Riemann surfaces. In: Analytic functions. Princeton: Princeton Univ. Press 1960 · Zbl 0100.28903
[5] Berger, M., Ebin, D.: Some decompositions of the space of symmetric tensors on a Riemannian manifold. J. Differential Geometry3, 379-392 (1969) · Zbl 0194.53103
[6] Bers, L.: Quasi conformal mappings and Teichmüller’s theorem. In: Analytic functions, pp. 89-120. Princeton: Princeton Univ. Press 1960 · Zbl 0100.28904
[7] Böhme, R., Tromba, A.: The index theorem for classical minimal surfaces. Ann. Math.113, 447-499 (1981) · Zbl 0482.58010 · doi:10.2307/2006993
[8] Earle, C.J., Eells, J.: A fibre bundle description of Teichmüller theory. J. Differential Geometry3, 19-43 (1969) · Zbl 0185.32901
[9] Ebin, D.: The manifold of Riemannian metrics. Proc. Symp. Pure Math. AMS15, 11-40 (1970) · Zbl 0205.53702
[10] Eisenhart, L.P.: Riemannian isometry. Princeton: Princeton Univ. Press 1966
[11] Fischer, A., Marsden, J.: Deformations of the scalar curvature. Duke Math. J.42, 519-547 (1975) · Zbl 0336.53032 · doi:10.1215/S0012-7094-75-04249-0
[12] Fischer, A., Marsden, J.: Manifolds of conformally equivalent metrics. Can. J. Math.29, 193-209 (1977) · Zbl 0358.58006 · doi:10.4153/CJM-1977-019-x
[13] Frankel, T.T.: On a theorem of Hurwitz and Bochner. J. Math. Mech.15, 373-377 (1966) · Zbl 0139.39103
[14] Heinz, E.: Über gewisse elliptische Systeme von Differentialgleichungen. Math. Ann.131, 411-428 (1956) · Zbl 0072.31103 · doi:10.1007/BF01350097
[15] Kobayashi, S., Nomizu, K.: Foundations of differential geometry. Vol. I and II. New York: Interscience 1963 · Zbl 0119.37502
[16] Newlander, A., Nirenberg, L.: Complex analytic coordinates in almost complex manifolds. Ann. Math.65, 391-404 (1957) · Zbl 0079.16102 · doi:10.2307/1970051
[17] Omori, H.: On the group of Diffeomorphisms on a compact manifold. Proc. Symp. Pure Math. AMS15, 167-183 (1970) · Zbl 0214.48805
[18] Palais, R.: The slice theorem. Unpublished · Zbl 1140.55001
[19] Palais, R.: Foundations of global non-linear analysis. New York: Benjamin 1968 · Zbl 0164.11102
[20] Rauch, H.: Theta functions with applications to Riemann surfaces. Baltimore: Williams and Wilkens 1974
[21] Teichmüller, O.: Extremale quasikonforme Abbildungen und quadratische Differentiale. Preuss. Acad. Math.-naturw. Kl. 22, 1940 · JFM 66.0232.03
[22] Teichmüller, O.: Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen. Preuss. Acad. Math.-naturw. Kl. 4 (1943) · Zbl 0060.23313
[23] Thurston, W.: The geometry and topology of 3-manifold. Lecture notes. Princeton Univ.
[24] Tromba, A.: Oriented infinite dimensional varieties, degree theory, and the Morse number of minimal surfaces spanning a curve in ?. Parts I and II (to appear) · Zbl 0604.58008
[25] Wolf, J.: Spaces of constant curvature. New York: Mc Graw Hill 1967 · Zbl 0162.53304
[26] Bergert, L.B., Bourguignon, J.P., Lafontaine, J.: Déformations localement triviales des variétés Riemanniennes. AMS Proc. Pure Math.27, 3-32 (1975)
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