The scalar curvature equation on 2- and 3-spheres

Sun Yung A. Chang, Matthew J. Gursky, Paul C. Yang

Research output: Contribution to journalArticle

170 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)205-229
Number of pages25
JournalCalculus of Variations and Partial Differential Equations
Volume1
Issue number2
DOIs
StatePublished - May 1 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Mathematics subject classifications: 35J60, 58G03

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