The Paneitz equation in hyperbolic space

Abstract

The Paneitz operator is a fourth order differential operator which arises in conformal geometry and satisfies a certain covariance property. Associated to it is a fourth order curvature – the Q-curvature.We prove the existence of a continuum of conformal radially symmetric complete metrics in hyperbolic space Hn, n>4, all having the same constant Q-curvature.Moreover, similar results can be shown also for suitable non-constant prescribed Q-curvature functions.