We study the conformal metrics on with constant -curvature having finite volume, particularly in the case . We show that when such metrics exist in if and only if . Moreover we study their asymptotic behavior at infinity, in analogy with the case , which we treated in a recent paper. When , we show that such metrics have the form , where is a polynomial such that and . In dimension , such metrics correspond to the polynomials of degree with .
Cite this article
Luca Martinazzi, Conformal metrics on ℝ<sup>2m</sup> with constant <em>Q</em>-curvature. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), no. 4, pp. 279–292DOI 10.4171/RLM/525