by Grunau, H.-Ch., Ould Ahmedou, M., Reichel, W..

**Series:** 2006-38, Preprints

- MSC:
- 35J60 Nonlinear elliptic equations
- 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions

**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 $\mathbb{H}^n$, $n>4$, all having

the same constant $Q$-curvature.

Moreover, similar results can be shown also for suitable non-constant

prescribed $Q$-curvature functions.

**Keywords:**

Paneitz equation, complete conformal metric, hyperbolic space, prescribed Q-curvature

**This paper was published in:**

Annales Inst. H. Poincare (C) Nonlinear Analysis 25, 847 - 864 (2008).