The Paneitz equation in hyperbolic space

By Hans-Christoph Grunau, M. Ahmedou, Wolfgang Reichel. 2008

47 citations recorded by the source corpus.

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 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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/d01dadc3fa27eac94fbdda497038db27b0bec6bb

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In Applied Mathematics

1. Mar'ia de Mar Gonz'alez
2. Valeria Banica
3. Mariel S'aez

Citations in the corpus

• Some constructions for the fractional Laplacian on noncompact manifolds (2012, background): “In [41], the authors study the Paneitz operator on hyperbolic space, that is a conformally covariant operator of order 4.”