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Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

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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 ≥ 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.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences de Sfax, Route Soukra, Sfax, Tunisia

    Mohamed Ben Ayed

  2. Faculté des Sciences et Techniques, Université de Nouakchott, 5026, Nouakchott, Mauritania

    Khalil El Mehdi

  3. The Abdus Salam ICTP, Mathematics Section, Strada Costiera 11, 34014, Trieste, Italy

    Mohamed Ben Ayed & Khalil El Mehdi

Authors
  1. Mohamed Ben Ayed
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  2. Khalil El Mehdi
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Correspondence to Mohamed Ben Ayed.

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Mathematics Subject Classification (2000): 35J60, 53C21, 58J05

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Ben Ayed, M., El Mehdi, K. Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature. manuscripta math. 114, 211–228 (2004). https://doi.org/10.1007/s00229-004-0463-z

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  • DOI: https://doi.org/10.1007/s00229-004-0463-z

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