On Conformal Paneitz Curvature Equations in Higher Dimensional Spheres

Abstract

We study the problem of prescribing the Paneitz curvature on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of such critical points at infinity, we prove some existence results.

29 pages

References in corpus (2)

• Prescribing a fourth order conformal invariant on the standard sphere, Part II: blow-up analysis and applications
• The Paneitz Curvature Problem on Lower Dimensional Spheres