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Transactions of the American Mathematical Society

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Courbures scalaires des variétés d'invariant conforme négatif


Author: Antoine Rauzy
Journal: Trans. Amer. Math. Soc. 347 (1995), 4729-4745
MSC: Primary 53C21; Secondary 35J60
DOI: https://doi.org/10.1090/S0002-9947-1995-1321588-5
MathSciNet review: 1321588
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Abstract: In this paper, we are interested in the problem of prescribing the scalar curvature on a compact riemannian manifold of negative conformal invariant. We give a necessary and sufficient condition when the prescribed function $ f$ is nonpositive. When $ \sup(f) > 0$, we merely find a sufficient condition. This is the subject of the first theorem. In the second one, we prove the multiplicity of the solutions of subcritical (for the Sobolev imbeddings) elliptic equations. In another article [8], we will prove the multiplicity of the solutions of the prescribing curvature problem, i.e. for a critical elliptic equation.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1321588-5
Article copyright: © Copyright 1995 American Mathematical Society