Annals of Global Analysis and Geometry

, Volume 7, Issue 2, pp 155–161 | Cite as

Complex structures in the Nash-Moser category

  • Jens Gravesen
Article

Abstract

Working in the Nash-Moser category, it is shown that the harmonic and holomorphic differentials and the Weierstrass points on a closed Riemann surface depend smoothly on the complex structure. It is also shown that the space of complex structures on any compact surface forms a principal bundle over the Teichmüller space and hence that the uniformization maps of the closed disk and the sphere depend smoothly on the complex structure.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. J. Eearle and J. Eells, Fibre Bundle Description of Teichmüller Theory, J. Differential Geometry3 (1969), 19–43.Google Scholar
  2. [2]
    C. J. Earle and A. Schatz, Teichmüller Theory for Surfaces With Boundary, J. Differential Geometry4 (1970), 169–185.Google Scholar
  3. [3]
    D. G. Ebin, The Manifold of Riemannian Metrics, in: Global Analysis, Proceedings of Symposia in Pure Mathematics 15, Amer. Math. Soc., Providence 1970.Google Scholar
  4. [4]
    H. M. Farkas and I. Kra, Riemann Surfaces, Springer Verlag, New York 1980.Google Scholar
  5. [5]
    J. Gravesen, Geometrical Methods in Quantum Field Theory, D. Phil. Thesis, Oxford, 1987; see also: On the topology of holomorphic maps, Acta Math.162 (1989), 247–286.Google Scholar
  6. [6]
    R. S. Hamilton, The Inverse Function Theorem of Nash and Moser, Bull. Amer. Math. Soc.7 (1982), 65–222.Google Scholar
  7. [7]
    T. N. Subramaniam, Slices for Actions of Infinite Dimensional Groups, in: Differential Analysis in Infinite Dimensional Spaces, Contemporary Mathematics 54, Amer. Math. Soc., Providence 1986, pp. 65–77.Google Scholar

Copyright information

© VEB Deutscher Verlag der Wissenschaften Berlin 1989

Authors and Affiliations

  • Jens Gravesen
    • 1
  1. 1.Mathematical InstituteThe Technical University of DenmarkLyngbyDenmark

Personalised recommendations