Abstract
We study conformal metrics gu=e2u|dx|2 on R2m with constant Q-curvature Qgu≡(2m−1)! (notice that (2m−1)! is the Q-curvature of S2m) and finite volume. When m=3 we show that there exists V⁎ such that for any V∈[V⁎,∞) there is a conformal metric gu=e2u|dx|2 on R6 with Qgu≡5! and vol(gu)=V. This is in sharp contrast with the four-dimensional case, treated by C.-S. Lin. We also prove that when m is odd and greater than 1, there is a constant Vm>vol(S2m) such that for every V∈(0,Vm] there is a conformal metric gu=e2u|dx|2 on R2m with Qgu≡(2m−1)!, vol(g)=V. This extends a result of A. Chang and W.-X. Chen. When m is even we prove a similar result for conformal metrics of negative Q-curvature.
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