An End to End Gluing Construction for Metrics of Constant Positive Scalar Curvature

Details An End to End Gluing Construction for Metrics of Constant Positive Scalar Curvature An End to End Gluing Construction for Metrics of Constant Positive Scalar Curvature

2002-01-17

arxiv.org/abs/math/0201166v1

Indiana Univ. Math. J. 52 (2003), 703-726

Mathematics

Differential Geometry

18 pages

Scientific paper

Complete constant positive scalar curvature metrics on S^n - {p_1, ..., p_k} admit a definite asymptotic structure; i.e. the metric is asymptotic to a specific S^{n-1}-invariant metric near the puncture points. This allows one to glue together two such metrics near their puncture points, provided the asymptotic structures match, and create a metric whose scalar curvature is very close to constant. In this paper we perturb this new metric to obtain a metric of constant scalar curvature.

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