JournalsaihpcVol. 25, No. 5pp. 847–864

The Paneitz equation in hyperbolic space

  • Mohameden Ould Ahmedou

    Mathematisches Institut, Eberhard-Karls-Universität, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

  • Hans-Christoph Grunau

    Fakultät für Mathematik, Otto-von-Guericke-Universität, Postfach 4120, D-39016 Magdeburg, Germany

  • Wolfgang Reichel

    Mathematisches Institut, Universität Gießen, Arndtstr. 2, D-35392 Gießen, Germany
The Paneitz equation in hyperbolic space cover
Download PDF

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 , , all having the same constant Q-curvature.

Moreover, similar results can be shown also for suitable non-constant prescribed Q-curvature functions.

Cite this article

Mohameden Ould Ahmedou, Hans-Christoph Grunau, Wolfgang Reichel, The Paneitz equation in hyperbolic space. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 5, pp. 847–864

DOI 10.1016/J.ANIHPC.2007.05.001