2009/11/23 by Almir Silva Santos, Santos, Almir Silva · 3 citations
Mathematics · #53A30 #53C21 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Constant (computer programming) #Curvature #Degenerate energy levels #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Physics #Pure mathematics #Quantum mechanics #Riemann curvature tensor #Riemannian manifold #Scalar curvature #Sectional curvature #Weyl tensor #Yamabe flow #math.AP #math.DG #msc:53A30 #msc:53C21
paper · pdf · doi:10.48550/arxiv.0911.4477
published in arXiv (Cornell University) (Cornell University) · 40 pages
arxiv created 2009/11/23 · openalex publication_date 2009/11/23 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It has been showed by Byde 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.