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

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.

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

References in corpus (1)

• Blow-up phenomena for scalar-flat metrics on manifolds with boundary

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• Solutions for a nonlocal elliptic equation involving critical growth and Hardy potential
• Uniformization Theorems: Between Yamabe and Paneitz
• The asymptotic behavior of Palais-Smale sequences on manifolds with boundary