The Paneitz equation in hyperbolic space

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


Preprint series: 06-38, Preprints

The paper is published: Annales Inst. H. Poincare (C) Nonlinear Analysis 25, 847 - 864 (2008).

35J60 Nonlinear PDE of elliptic type
53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions, See also {58G30}


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

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Letzte Änderung: 01.03.2018 - Ansprechpartner:

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