An End to End Gluing Construction for Metrics of Constant Positive Scalar Curvature
Differential Geometry
2010-06-14 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.math/0201166,
title = {An End to End Gluing Construction for Metrics of Constant Positive Scalar Curvature},
author = {Jesse Ratzkin},
journal= {arXiv preprint arXiv:math/0201166},
year = {2010}
}
Comments
18 pages