On the higher order conformal covariant operators on the sphere

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We will show that in the conformal class of the standard metric gs n on Sn, the scaling invariant functional (μg(Sn)) 2m-n/nSnQ2m, gg maximizes at gsn when n is odd and m = n-1/2 or n+3/2. For n odd and m ≥ n+5/2, gsn is not stable and the functional has no local maximizer. Here Q2m,g is the 2mth order Q-curvature.

Original languageEnglish (US)
Pages (from-to)279-299
Number of pages21
JournalCommunications in Contemporary Mathematics
Issue number3
StatePublished - Jun 2007


  • Approximation in Sobolev spaces
  • Conformal convariant operators
  • Q-curvature
  • Sharp Sobolev inequalities

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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