Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

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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.
20 pages

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Analysis of PDEs, 35J60; 53C21; 58J05

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http://salesiana.dossiersoluciones.com/handle/123456789/67462

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305199
 http://arxiv.org/abs/math/0305199

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arXiv