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Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

Mohamed Ben Ayed·Khalil El Mehdi
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Abstract

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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Mohamed Ben Ayed, Khalil El Mehdi. 2004-03-18. Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature. https://arxiv.org/abs/math/0305199

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