Acta Mathematica

Prescribing Gaussian curvature on S2

Sun-yung Alice Chang and 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.

Article information

Acta Math. Volume 159 (1987), 215-259.

Received: 3 September 1986
Revised: 7 January 1987
First available in Project Euclid: 31 January 2017

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1987 © Almqvist & Wiksell


Chang, Sun-yung Alice; Yang, Paul C. Prescribing Gaussian curvature on S 2. Acta Math. 159 (1987), 215--259. doi:10.1007/BF02392560.

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  • 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.
  • Aubin, T., The scalar curvature in differential geometry and relativity. Holland 1976, pp. 5–18.
  • 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.
  • Chang, S. Y. A. & Yang, P. C., Conformal deformation of metric on S2. To appear in Journal of Diff. Geometry.
  • Escobar, J. F. & Schoen, R., Conformal metrics with prescribed scalar curvature. Preprint.
  • Hartman, P., Ordinary differential equations. Basel Birkhäuser (1982).
  • Hersch, J., Quatre propriétés isopérimétriques de membranes sphériques homogènes. C. R. Acad. Sci. Paris Ser. I, 270 (1970), 1645–1648.
  • Hong, C. W., A best constant and the Gaussian curvature. Preprint.
  • Kazdan, J. & Warner, F., Curvature functions for compact 2-manifold. Ann. of Math. (2), 99 (1974), 14–47.
  • — Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvature. Ann. of Math. (2), 101 (1975), 317–331.
  • Moser, J., A sharp form of an inequality by N. Trudinger. Indiana Univ. Math. J., 20 (1971), 1077–1091.
  • — On a non-linear problem in differential geometry. Dynamical Systems (M. Peixoto, editor), Academic Press, N.Y. (1973).
  • Mostow, G. D., Some new decomposition theorems for semi-simple groups. Mem. Amer. Math. Soc., 14 (1955).
  • Onofri, E., On the positivity of the effective action in a theory of random surface. Comm. Math. Phys., 86 (1982), 321–326.
  • Onofri, E. & Virasoro, M., On a formulation of Polyakov's string theory with regular classical solutions. Nuclear Phys. B, 201 (1982), 159–175.
  • Schoen, R., Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differential Geom., 20 (1985), 479–495.