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 asymptotics 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.
展开▼
