The Nirenberg problem and its generalizations: a unified approach

Tianling Jin, Yan Yan Li, Jingang Xiong

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations Pσ(v)=Kvn+2σn-2σ on the standard unit sphere Sn for all σ∈ (0 , n/ 2) , where Pσ is the intertwining operator of order 2 σ. Finding positive solutions of these equations is equivalent to seeking metrics in the conformal class of the standard metric on spheres with prescribed certain curvatures. When σ= 1 , it is the prescribing scalar curvature problem or the Nirenberg problem, and when σ= 2 , it is the prescribing Q-curvature problem.

Original languageEnglish (US)
Pages (from-to)109-151
Number of pages43
JournalMathematische Annalen
Volume369
Issue number1-2
DOIs
StatePublished - Oct 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • 35B44
  • 35G20
  • 45M20
  • 53C21

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