Conformally Euclidean metrics on ℝn with arbitrary total Q-curvature

where $Q \geq 0$ , $κ \in (0, \infty)$ and $n \geq 3$ . Using ODE techniques, Martinazzi (for $n = 6$ ) and Huang and Ye (for $n = 4 m + 2$ ) proved the existence of a solution to the above problem with $Q \equiv constant > 0$ and for every $κ \in (0, \infty)$ . We extend these results in every dimension $n \geq 5$ , thus completely answering the problem opened by Martinazzi. Our approach also extends to the case in which $Q$ is nonconstant, and under some decay assumptions on $Q$ we can also treat the cases $n = 3$ and $n = 4$ .

Keywords

$Q$-curvature, nonlocal equation, conformal geometry

Mathematical Subject Classification 2010

Primary: 35G20, 35R11, 53A30

Milestones

Received: 5 August 2016

Revised: 8 November 2016

Accepted: 22 January 2017

Published: 17 April 2017

Authors

Ali Hyder
Departement Mathematik und Informatik Universität Basel CH-4051 Basel Switzerland

Vol. 10, No. 3, 2017

Ali Hyder

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors