Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

Details Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

2003-05-14

arxiv.org/abs/math/0305199v4

Mathematics

Analysis of PDEs

20 pages

Scientific paper

In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the $n$-sphere, with $n\geq 5$. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given positive function under which we prove the existene of a metric, conformally equivalent to the standard metric, with prescribed Paneitz curvature.

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