Skip to main content
SpringerLink
Log in

Deformations of Riemann surfaces

  • Geometric and Qualitative Aspects of Analysis
  • Conference paper
  • First Online:
Lectures in Modern Analysis and Applications I

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 103))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. V. Ahlfors, The complex analytic structure of the space of closed Riemann surfaces. Analytic Functions. Princeton 1960, 45–66.

    Google Scholar 

  2. -, Some remarks on Teichmüller's space of Riemann surfaces. Ann. of Math. 74 (1961), 171–191.

    Article  MathSciNet  MATH  Google Scholar 

  3. -, Curvature properties of Teichmüller's space. J. Analyse Math. 9 (1961), 166–176.

    Article  MathSciNet  Google Scholar 

  4. -L. V. Ahlfors, Teichüller's spaces. Proc. Inter. Cong. Math. Stockholm 1962, 3–9.

    Google Scholar 

  5. -L. V. Ahlfors, Lectures on quasiconformal mappings. Mathematical Studies No. 10. Van Nostrand. 1966.

    Google Scholar 

  6. L. V. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics. Ann. of Math. 72 (1960), 385–404.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. I. Al'ber, On n-dimensional problems in the calculus of variations in the large. Soviet Math. 51 (1964), 700–704.

    Google Scholar 

  8. A. Andreotti, On a theorem of Torelli. Amer. J. Math. 80 (1958), 801–828.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. A. Armstrong, The fundamental group of the orbit space of a discontinuous group. Proc. Camb. Phil. Soc. 64 (1968), 299–301.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Baer, Kurventypen auf Flächen. J. reine angew. Math. 156 (1927), 231–246.

    MATH  Google Scholar 

  11. -, Isotopie von Kurven auf orientierbaren, geschlossenen Flächen und ihr Zusammenhang mit der topologischei Deformation der Flächen. J. reine angew. Math. 159 (1928). 101–111.

    MATH  Google Scholar 

  12. W. L. Baily, Jr., On the moduli of Jacobian varieties. Ann. of Math. 71 (1960), 303–314.

    Article  MathSciNet  MATH  Google Scholar 

  13. -L. Bers, Spaces of Riemann surfaces. Proc Inter. Cong. Math. 1958, 349–361.

    Google Scholar 

  14. -L. Bers, Quasiconformal mappings and Teichmüller's theorem. Analytic Functions. Princeton 1960, 349–361.

    Google Scholar 

  15. -, Correction to “Spaces of Riemann surfaces as bounded domains”, Bull. Am. Math. 67 (1961), 465–466.

    Article  MathSciNet  Google Scholar 

  16. -, Simultaneous uniformization. Bull. Am. Math. Soc. 66 (1960), 94–97.

    Article  MathSciNet  MATH  Google Scholar 

  17. -, Inequalities for finitely generated Kleinian groups. J. Analyse Math. 18 (1967), 23–41.

    Article  MathSciNet  MATH  Google Scholar 

  18. -L. Bers, On moduli of Riemann surfaces. Notes at E.T.H. Zürich 1964.

    Google Scholar 

  19. L. Bers and L. Ehrenpreis, Holomorphic convexity of Teichmüller spaces. Bull. Am. Math. Soc. 70 (1964), 761–764.

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Busemann, Spaces with non-positive curvature. Acta Math. 80 (1948–49), 259–310.

    Article  MathSciNet  Google Scholar 

  21. H. Cartan, Quotient d'un espace analytique par un groupe d'automorphismes. Algebraic geometry and topology. Princeton 1957, 90–102.

    Google Scholar 

  22. C. J. Earle, The Teichmüller spaces for an arbitrary Fuchsian group. Bull. Am. Math. Soc. 70 (1964), 699–701.

    Article  MathSciNet  MATH  Google Scholar 

  23. -C. J. Earle, The contractibility of certain Teichmüller spaces.

    Google Scholar 

  24. C. J. Earle, On holomorphic cross-sections in Teichmüller spaces.

    Google Scholar 

  25. C. J. Earle, and J. Ells, On the differential geometry of Teichmüller spaces J. Analyse Math. 19 (1967), 35–52.

    Article  MathSciNet  MATH  Google Scholar 

  26. -, The diffeomorphism group of a compact Riemann surface. Bull. Am. Math. Soc. 73 (1967), 557–559.

    Article  MathSciNet  Google Scholar 

  27. -, Foliations and fibrations. J. Diff. Geometry 1 (1967), 33–41.

    MathSciNet  MATH  Google Scholar 

  28. -C. J. Earle, A fibre bundle description of Teichmüller theory.

    Google Scholar 

  29. C. J. Earle and A. Schatz, Teichmüller theory for surfaces with boundary.

    Google Scholar 

  30. J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds. Am. J. Math. 86 (1964), 109–160.

    Article  MathSciNet  MATH  Google Scholar 

  31. D. B. A. Epstein, Curves on 2-manifolds and isotopies Acta Math. 115 (1966), 83–107.

    Article  MathSciNet  MATH  Google Scholar 

  32. H. Farkas, Special divisors and analytic subloci of Teichmüller space. Am. J. Math. 88 (1966), 881–901. Also, 89 (1967), 225.

    Article  MathSciNet  Google Scholar 

  33. A. M. Garsia, An imbedding of closed Riemann surfaces in Euclidean space. Comm. Math. Helv. 35 (1961), 93–110.

    Article  MathSciNet  MATH  Google Scholar 

  34. -, On the conformal type of algebraic surfaces of Euclidean space. Comm. Math. Helv. 37 (1962–63), 49–60.

    Article  MathSciNet  Google Scholar 

  35. A. M. Garsia and E. Rodemich, An embedding of Riemann surfaces of genus one. Pac. J. Math. 11 (1961), 193–204.

    Article  MathSciNet  MATH  Google Scholar 

  36. H. Grauert, Analytische Faserungen über holomorphvollstandigen Räumen. Math. Ann. 135 (1958), 263–273.

    Article  MathSciNet  MATH  Google Scholar 

  37. A. Grothendieck, Techniques de construction en géométrie analytique. Sém. H. Cartan. E. N. S. (1960/1), Exposé 7.

    Google Scholar 

  38. P. Hartman, On homotopic harmonic maps. Canad. J. Math. 19 (1967), 673–687.

    Article  MathSciNet  MATH  Google Scholar 

  39. E. Heinz, Über gewisse elliptische Systeme von Differentialgleichungen. Math. Ann. 131 (1956), 411–428.

    Article  MathSciNet  MATH  Google Scholar 

  40. A. Hurwitz, Über algebraische Gebilde mit eindeutigen Transformationen in sich. Math. Ann. 41 (1893), 403–442.

    Article  MathSciNet  MATH  Google Scholar 

  41. D. Husemoller, Fibre Bundles. McGraw Hill 1966.

    Google Scholar 

  42. K. Kodaira and D. C. Spencer, On deformations of complex analytic structures I, II, Ann. of Math. 67 (1958), 328–466.

    Article  MathSciNet  MATH  Google Scholar 

  43. S. Kravetz, On the geometry of Teichmüller spaces and the structure of their modular groups. Ann. Acad. Sci. Fenn. 278 (1959), 1–35.

    MathSciNet  Google Scholar 

  44. H. Lewy, On the non-vanishing of the Jacobian in certain one-to-one mappings. Bull. Am. Math. Soc. 42 (1936), 689–692.

    Article  MathSciNet  Google Scholar 

  45. W. B. R. Lickorish, A finite set of generators for the homeotopy group of a 2-manifold. Proc. Camb. Phil. Soc. 60 (1964), 769–778. Also, 62 (1966), 679–681.

    Article  MathSciNet  MATH  Google Scholar 

  46. A. M. MacBeath, On a theorem of J. Nielsen. Quart. J. Math. Oxford 13 (1962), 235–236.

    Article  MathSciNet  MATH  Google Scholar 

  47. W. Magnus, Über Automorphismen von Fundamentalgruppen barandeter Flächen. Math. Ann. 109 (1933/4), 617–646.

    Article  MathSciNet  Google Scholar 

  48. D. Mumford, Abelian quotients of the Teichmüller modular group. J. Analyse Math. 18 (1967), 227–244.

    Article  MathSciNet  MATH  Google Scholar 

  49. J. Nielsen, Abbildungsklassen endlicher Ordnung. Acta Math. 75 (1943), 23–115.

    Article  MathSciNet  Google Scholar 

  50. H. E. Rauch, On the transcendental moduli of algebraic Riemann surfaces. Proc. Nat. Acad. Sci. 41 (1955), 42–49.

    Article  MathSciNet  MATH  Google Scholar 

  51. -, On the moduli of Riemann surfaces. Proc. Nat. Acad. Sci. 41 (1955), 236–238.

    Article  MathSciNet  Google Scholar 

  52. -, Weierstrass points, branch points, and the moduli of Riemann surfaces. Comm. Pure Appl. Math. 12 (1959), 543–560.

    Article  MathSciNet  Google Scholar 

  53. -, Singularities of the modulus space. Bull. Am. Math. Soc. 68 (1962), 390–394.

    Article  MathSciNet  MATH  Google Scholar 

  54. -, A transcendental view of the space of algebraic Riemann surfaces. Bull. Am. Math. Soc. 71 (1965), 1–39.

    Article  MathSciNet  MATH  Google Scholar 

  55. J. H. Sampson, (to be published).

    Google Scholar 

  56. K. Shibata, On the existence of a harmonic mapping. Osaka Math. J. 15 (1963), 173–211.

    MathSciNet  MATH  Google Scholar 

  57. S. Smale, Diffeomorphisms of the 2-sphere. Proc. Am. Math. Soc. 10 (1959), 621–626.

    MathSciNet  MATH  Google Scholar 

  58. N. E. Steenrod, The topology of fibre bundles. Princeton 1951.

    Google Scholar 

  59. O. Teichmüller, Extremale quasikonfome Abbildungen und quadratische Differentiale. Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 22 (1939).

    Google Scholar 

  60. A. Weil, Modules des surfaces de Riemann. Sém. Bourbaki. 1958. Exp. 168.

    Google Scholar 

  61. H. H. Wu, Normal families of holomorphic mappings. Acta Math. 119 (1967), 193–233.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Clifford J. Earle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James Eells
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

C. T. Taam

Rights and permissions

Reprints and permissions

Copyright information

© 1969 Springer-Verlag

About this paper

Cite this paper

Earle, C.J., Eells, J. (1969). Deformations of Riemann surfaces. In: Taam, C.T. (eds) Lectures in Modern Analysis and Applications I. Lecture Notes in Mathematics, vol 103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099988

Download citation

  • DOI: https://doi.org/10.1007/BFb0099988

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04622-6

  • Online ISBN: 978-3-540-36145-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation