Conformal metrics on with constant -curvature
Luca Martinazzi
Rutgers University, Piscataway, Switzerland
![Conformal metrics on $ℝ^{2m}$ with constant $Q$-curvature cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rlm-volume-19-issue-4.png&w=3840&q=90)
Abstract
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 with constant -curvature. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), no. 4, pp. 279–292
DOI 10.4171/RLM/525