Conformal metrics on $\R^{2m}$ with constant Q-curvature
| dc.creator | Martinazzi, Luca | |
| dc.date | 2008-05-06 | |
| dc.date.accessioned | 2026-07-07T12:58:46Z | |
| dc.date.available | 2026-07-07T12:58:46Z | |
| dc.description | We study the conformal metrics on $\R^{2m}$ with constant Q-curvature $Q$ having finite volume, particularly in the case $Q\leq 0$. 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=0, we show that such metrics have the form $e^{2p}g_{\R^{2m}}$, where $p$ is a polynomial such that $2\leq °p\leq 2m-2$ and $\sup_{\R^{2m}}p<+\infty$. In dimension 4, such metrics are exactly the polynomials $p$ of degree 2 with $\lim_{|x|\to+\infty}p(x)=-\infty$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0805.0749 | |
| dc.identifier | http://arxiv.org/abs/0805.0749 | |
| dc.identifier | Rend. Lincei. Mat Appl. 19 (2008), 279-292 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225353 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.title | Conformal metrics on $\R^{2m}$ with constant Q-curvature | |
| dc.type | text |