The scalar curvature equation on 2- and 3-spheres

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

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

35J60 58G03 

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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

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