Prescribed scalar curvature on then-sphere

  • Richard Schoen
  • Dong Zhang

DOI: 10.1007/BF01322307

Cite this article as:
Schoen, R. & Zhang, D. Calc. Var (1996) 4: 1. doi:10.1007/BF01322307


This paper considers the prescribed scalar curvature problem onSn forn>-3. We consider the limits of solutions of the regularization obtained by decreasing the critical exponent. We characterize those subcritical solutions which blow up at the least possible energy level, determining the points at which they can concentrate, and their Morse indices. We then show that forn=3 this is the only blow up which can occur for solutions. We use this in combination with the Morse inequalities for the subcritical problem to obtain a general existence theorem for the prescribed scalar curvature problem onS3.

Mathematics subject classification (1991)

53C21 58E11 

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Richard Schoen
    • 1
  • Dong Zhang
    • 2
  1. 1.Mathematics DepartmentStanford UniversityStanfordUSA
  2. 2.Mathematics DepartmentJohns Hopkins UniversityBaltimoreUSA

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