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

Jesse Ratzkin
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Abstract

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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Jesse Ratzkin. 2002-01-17. An End to End Gluing Construction for Metrics of Constant Positive Scalar Curvature. https://arxiv.org/abs/math/0201166

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