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Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

Authors:	Mohamed?Ben Ayed mailto:Mohamed.Benayed@fss.rnu.tn,elmehdik@ictp.trieste.it" title=" Mohamed.Benayed@fss.rnu.tn,elmehdik@ictp.trieste.it" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Khalil?El Mehdi

Affiliation:	(1) Département de Mathématiques, Faculté des Sciences de Sfax, Route Soukra, Sfax, Tunisia;(2) Faculté des Sciences et Techniques, Université de Nouakchott, 5026, Nouakchott, Mauritania;(3) The Abdus Salam ICTP, Mathematics Section, Strada Costiera 11, 34014 Trieste, Italy

Abstract:	In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the n-sphere, with n 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 existence of a metric, conformally equivalent to the standard metric, with prescribed Paneitz curvature.Mathematics Subject Classification (2000): 35J60, 53C21, 58J05Send offprint requests to: Khalil El Mehdi

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