English

Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow

Differential Geometry 2015-08-07 v3 Analysis of PDEs

Abstract

We study a conformal flow for compact Riemannian manifolds of dimension greater than two with boundary. Convergence to a scalar-flat metric with constant mean curvature on the boundary is established in dimensions up to seven, and in any dimensions if the manifold is spin or if it satisfies a generic condition.

Keywords

Cite

@article{arxiv.1206.1184,
  title  = {Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow},
  author = {Sergio Almaraz},
  journal= {arXiv preprint arXiv:1206.1184},
  year   = {2015}
}

Comments

Title slightly changed. Introduction improved and changed to include the recent results (arXiv:1407.0673) on Conjecture 1.5. Appendix C removed and published as a separate paper (arXiv:1508.01058). Although Appendix B was shortened for publication, this arxiv version remains complete and unchanged. Some typos corrected. 71 pages