Constant scalar curvature on open manifolds with finite volume
Commun. Korean Math. Soc. 1997 Vol. 12, No. 1, 101-108
Seongtag Kim
Sung Kyun Kwan University
Abstract : We let $(M,g)$ be a noncompact complete Riemannian manifold of dimension $n \ge 3$ with finite volume and positive scalar curvature. We show the existence of a conformal metric with constant positive scalar curvature on $(M,g)$ by gluing solutions of Yamabe equation on each compact subsets $K_i$ with $ \cup K_i =M $.
Keywords : Scalar curvature, complete manifolds, conformal metric
MSC numbers : 53C21
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