Advertisement

Acta Mathematica

, Volume 159, Issue 1, pp 215–259 | Cite as

Prescribing Gaussian curvature on S2

  • Sun-yung Alice Chang
  • Paul C. Yang
Article

Keywords

Gaussian Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Aubin, T., Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire par la transformation conforme de la courbure scalaire.J. Funct. Anal., 32 (1979), 148–174.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    Aubin, T.,The scalar curvature in differential geometry and relativity. Holland 1976, pp. 5–18.Google Scholar
  3. [3]
    Bahri, A. &Coron, J. M., Une théorie des points critiques à l'infini pour l'equation de Yamabe et le problème de Kazdan-Warner.C. R. Acad. Sci. Paris Sér. I, 15 (1985), 513–516.MathSciNetGoogle Scholar
  4. [4]
    Chang, S. Y. A. & Yang, P. C., Conformal deformation of metric onS 2. To appear inJournal of Diff. Geometry.Google Scholar
  5. [5]
    Escobar, J. F. & Schoen, R., Conformal metrics with prescribed scalar curvature. Preprint.Google Scholar
  6. [6]
    Hartman, P.,Ordinary differential equations. Basel Birkhäuser (1982).Google Scholar
  7. [7]
    Hersch, J., Quatre propriétés isopérimétriques de membranes sphériques homogènes.C. R. Acad. Sci. Paris Ser. I, 270 (1970), 1645–1648.MATHMathSciNetGoogle Scholar
  8. [8]
    Hong, C. W., A best constant and the Gaussian curvature. Preprint.Google Scholar
  9. [9]
    Kazdan, J. &Warner, F., Curvature functions for compact 2-manifold.Ann. of Math. (2), 99 (1974), 14–47.CrossRefMathSciNetGoogle Scholar
  10. [10]
    — Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvature.Ann. of Math. (2), 101 (1975), 317–331.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    Moser, J., A sharp form of an inequality by N. Trudinger.Indiana Univ. Math. J., 20 (1971), 1077–1091.CrossRefMATHGoogle Scholar
  12. [12]
    — On a non-linear problem in differential geometry.Dynamical Systems (M. Peixoto, editor), Academic Press, N.Y. (1973).Google Scholar
  13. [13]
    Mostow, G. D., Some new decomposition theorems for semi-simple groups.Mem. Amer. Math. Soc., 14 (1955).Google Scholar
  14. [14]
    Onofri, E., On the positivity of the effective action in a theory of random surface.Comm. Math. Phys., 86 (1982), 321–326.CrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    Onofri, E. &Virasoro, M., On a formulation of Polyakov's string theory with regular classical solutions.Nuclear Phys. B, 201 (1982), 159–175.CrossRefMathSciNetGoogle Scholar
  16. [16]
    Schoen, R., Conformal deformation of a Riemannian metric to constant scalar curvature.J. Differential Geom., 20 (1985), 479–495.MathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksell 1987

Authors and Affiliations

  • Sun-yung Alice Chang
    • 1
  • Paul C. Yang
    • 2
  1. 1.University of CaliforniaLos AngelesUSA
  2. 2.University of Southern CaliforniaLos AngelesUSA

Personalised recommendations