Conformal deformations of integral pinched 3-manifolds |
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Authors: | Giovanni Catino |
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Institution: | a SISSA, Via Beirut 2-4, 34014 Trieste, Italy b Institut Fourier, Université Grenoble 1, 100 rue des Maths, F38402 Saint-Martin d'Hères Cedex, France |
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Abstract: | In this paper we prove that, under an explicit integral pinching assumption between the L2-norm of the Ricci curvature and the L2-norm of the scalar curvature, a closed 3-manifold with positive scalar curvature admits a conformal metric of positive Ricci curvature. In particular, using a result of Hamilton, this implies that the manifold is diffeomorphic to a quotient of S3. The proof of the main result of the paper is based on ideas developed in an article by M. Gursky and J. Viaclovsky. |
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Keywords: | 53C24 53C20 53C21 53C25 |
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