An end-to-end gluing construction for metrics of constant positive scalar curvature

Abstract

Complete, constant positive scalar curvature metrics on S n {p 0 ,...,p k } admit a definite asymptotic structure, i.e., the metric is asymptotically S n-1 -invariant near each puncture. This allows one to glue together two such metrics near their punctures, provided the asyrnptotics match, and create a metric whose scalar curvature is nearly constant. In this paper we perturb this new metric to obtain a new metric with constant scalar curvature.