A Construction of Constant Scalar Curvature Manifolds with Delaunay-type Ends |
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Authors: | Almir Silva Santos |
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Affiliation: | 1. Departamento de Matemática, Centro de Ciências Exatas e Tecnologia, Universidade Federal de Sergipe, Av. Marechal Rondon s/n, S?o Cristóv?o, SE, 49100-000, Brazil 2. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil
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Abstract: | It has been showed by Byde (Indiana Univ. Math. J. 52(5):1147–1199, 2003) that it is possible to attach a Delaunay-type end
to a compact nondegenerate manifold of positive constant scalar curvature, provided it is locally conformally flat in a neighborhood
of the attaching point. The resulting manifold is noncompact with the same constant scalar curvature. The main goal of this
paper is to generalize this result. We will construct a one-parameter family of solutions to the positive singular Yamabe
problem for any compact non-degenerate manifold with Weyl tensor vanishing to sufficiently high order at the singular point.
If the dimension is at most 5, no condition on the Weyl tensor is needed. We will use perturbation techniques and gluing methods. |
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