Prescribing the scalar curvatureproblem on higher-dimensional manifolds

Randa Ben Mahmoud; Hichem Chtioui

doi:10.3934/dcds.2012.32.1857

Article Contents

2012, Volume 32, Issue 5: 1857-1879. Doi: 10.3934/dcds.2012.32.1857

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Prescribing the scalar curvature problem on higher-dimensional manifolds

Randa Ben Mahmoud^1, and
Hichem Chtioui^2,

1.
Department of Mathematics, Faculty of Sciences of Sfax, Route of Soukra, Sfax
2.
Department of mathematics, King Abdulaziz university, P.O. 80230, Jeddah

Received: November 2010

Revised: July 2011

Published: May 2012

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Abstract

In this paper we consider the problem of existence of conformal metrics with prescribed scalar curvature on n-dimensional Riemannian manifolds, $n \geq 5 $. Using precise estimates on the losses of compactness, we characterize the critical points at infinity of the associated variational problem and we prove existence results for curvatures satisfying an assumption of Bahri-Coron type.

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Mathematics Subject Classification: 58E05, 35J65, 35C21, 35B40.

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References

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