Conformal metrics on R-2m with constant Q-curvature Luca Martinazzi

We study the conformal metrics on R-2m with constant Q-curvature Q is an element of R having finite volume, particularly in the case Q <= 0. We show that when Q < 0 such metrics exist in R-2m if and only if m > 1. Moreover, we study their asymptotic behavior at infinity, in analogy with the case Q > 0, which we treated in a recent paper. When Q D 0, we show that such metrics have the form e(2p) g(R2m), where p is a polynomial such that 2 <= deg p <= 2 m 2 and sup(R2m) p < infinity. In dimension 4, such metrics correspond to the polynomials p of degree 2 with lim(|x|->infinity) p(x) = -infinity.