Calculus of Variations and Partial Differential Equations

, Volume 1, Issue 2, pp 205–229

The scalar curvature equation on 2- and 3-spheres

  • Sun-Yung A. Chang
  • Matthew J. Gursky
  • Paul C. Yang
Article

DOI: 10.1007/BF01191617

Cite this article as:
Chang, SY.A., Gursky, M.J. & Yang, P.C. Calc. Var (1993) 1: 205. doi:10.1007/BF01191617

Abstract

In this article we obtain a priori estimates for solutions to the prescribed scalar curvature equation on 2- and 3-spheres under a nondegeneracy assumption on the curvature function. Using this estimate, we use the continuity method to demonstrate the existence of solutions to this equation when a map associated to the given curvature function has non-zero degree.

Mathematics subject classifications

35J6058G03

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Sun-Yung A. Chang
    • 1
  • Matthew J. Gursky
    • 2
  • Paul C. Yang
    • 3
  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA
  3. 3.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  4. 4.Institute for Advanced StudyPrincetonUSA