Conformal metrics on R^{2m} with constant Q-curvature

Martinazzi, Luca. (2008) Conformal metrics on R^{2m} with constant Q-curvature. Rendiconti Lincei. Matematica e Applicazioni, 19 (4). pp. 279-292.

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Official URL: http://edoc.unibas.ch/49851/

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We study the conformal metrics on \R2m with constant Q-curvature Q∈\R having finite volume, particularly in the case Q≤0. We show that when Q<0 such metrics exist in \R2m 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=0, we show that such metrics have the form e2pg\R2m, where p is a polynomial such that 2≤degp≤2m−2 and sup\R2mp<+∞. In dimension 4, such metrics correspond to the polynomials p of degree 2 with lim|x|→+∞p(x)=−∞.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik
UniBasel Contributors:Martinazzi, Luca
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:European Mathematical Society
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:19 Dec 2017 10:00
Deposited On:19 Dec 2017 10:00

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