Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

Author: Ben Ayed Mohamed  

Publisher: Springer Publishing Company

ISSN: 0025-2611

Source: manuscripta mathematica, Vol.114, Iss.2, 2004-06, pp. : 211-228

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

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.