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| Various prescribing curvature problems on a manifold can be expressed as follows: given a smooth positive function K defined on M with the metric g, can one find a conformal metric such that the aforementioned curvature is equal to K ? The typical example is the prescribing scalar curvature problem on the standard sphere. In this talk we give some existence results under flatness and non degeneracy conditions. In particular we extend the well known existence results of Bahri-Coron and Y.Y. Li. |
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