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2006-38

The Paneitz equation in hyperbolic space

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).