A compactness theorem for scalar-flat metrics on manifolds with boundary |
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Authors: | S��rgio de Moura Almaraz |
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Affiliation: | 1. Instituto de Matem??tica, Universidade Federal Fluminense (UFF), Rua M??rio Santos Braga S/N, Niter??i, RJ, 24020-140, Brazil
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Abstract: | Let (M n , g) be a compact Riemannian manifold with boundary ?M. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have ?M as a constant mean curvature hypersurface. We prove that this set is compact for dimensions n ?? 7 under the generic condition that the trace-free 2nd fundamental form of ?M is nonzero everywhere. |
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