TY - JOUR
T1 - On the higher order conformal covariant operators on the sphere
AU - Hang, Fengbo
N1 - Funding Information:
The research of the author is supported by National Science Foundation Grant DMS-0209504. We would like to thank Paul Yang for valuable discussions.
PY - 2007/6
Y1 - 2007/6
N2 - 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.
AB - 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.
KW - Approximation in Sobolev spaces
KW - Conformal convariant operators
KW - Q-curvature
KW - Sharp Sobolev inequalities
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U2 - 10.1142/S0219199707002435
DO - 10.1142/S0219199707002435
M3 - Article
AN - SCOPUS:34347351036
SN - 0219-1997
VL - 9
SP - 279
EP - 299
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
IS - 3
ER -