An End to End Gluing Construction for Metrics of Constant Positive Scalar Curvature
Abstract
Complete constant positive scalar curvature metrics on Sn - p1, ..., pk admit a definite asymptotic structure; i.e. the metric is asymptotic to a specific Sn-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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