We will show that in the conformal class of the standard metric gs n on Sn, the scaling invariant functional (μg(Sn)) 2m-n/n∫SnQ2m, gdμg 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.
- Approximation in Sobolev spaces
- Conformal convariant operators
- Sharp Sobolev inequalities
ASJC Scopus subject areas
- Applied Mathematics