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Prescribing Gaussian curvature on S2

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Acta Mathematica

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References

  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.

    Article  MATH  MathSciNet  Google Scholar 

  2. Aubin, T.,The scalar curvature in differential geometry and relativity. Holland 1976, pp. 5–18.

  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.

    MathSciNet  Google Scholar 

  4. Chang, S. Y. A. & Yang, P. C., Conformal deformation of metric onS 2. To appear inJournal of Diff. Geometry.

  5. Escobar, J. F. & Schoen, R., Conformal metrics with prescribed scalar curvature. Preprint.

  6. Hartman, P.,Ordinary differential equations. Basel Birkhäuser (1982).

    Google Scholar 

  7. Hersch, J., Quatre propriétés isopérimétriques de membranes sphériques homogènes.C. R. Acad. Sci. Paris Ser. I, 270 (1970), 1645–1648.

    MATH  MathSciNet  Google Scholar 

  8. Hong, C. W., A best constant and the Gaussian curvature. Preprint.

  9. Kazdan, J. &Warner, F., Curvature functions for compact 2-manifold.Ann. of Math. (2), 99 (1974), 14–47.

    Article  MathSciNet  Google Scholar 

  10. — Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvature.Ann. of Math. (2), 101 (1975), 317–331.

    Article  MATH  MathSciNet  Google Scholar 

  11. Moser, J., A sharp form of an inequality by N. Trudinger.Indiana Univ. Math. J., 20 (1971), 1077–1091.

    Article  MATH  Google Scholar 

  12. — On a non-linear problem in differential geometry.Dynamical Systems (M. Peixoto, editor), Academic Press, N.Y. (1973).

    Google Scholar 

  13. Mostow, G. D., Some new decomposition theorems for semi-simple groups.Mem. Amer. Math. Soc., 14 (1955).

  14. Onofri, E., On the positivity of the effective action in a theory of random surface.Comm. Math. Phys., 86 (1982), 321–326.

    Article  MATH  MathSciNet  Google Scholar 

  15. Onofri, E. &Virasoro, M., On a formulation of Polyakov's string theory with regular classical solutions.Nuclear Phys. B, 201 (1982), 159–175.

    Article  MathSciNet  Google Scholar 

  16. Schoen, R., Conformal deformation of a Riemannian metric to constant scalar curvature.J. Differential Geom., 20 (1985), 479–495.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of California, Los Angeles, CA, USA

    Sun-yung Alice Chang

  2. University of Southern California, Los Angeles, CA, USA

    Paul C. Yang

Authors
  1. Sun-yung Alice Chang
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  2. Paul C. Yang
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Research supported in part by N.S.F. grants and the Forschungsinstitut für Mathematik, E.T.H. Zürich, Switzerland.

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Chang, Sy.A., Yang, P.C. Prescribing Gaussian curvature on S2 . Acta Math. 159, 215–259 (1987). https://doi.org/10.1007/BF02392560

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  • DOI: https://doi.org/10.1007/BF02392560

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