arXiv:1206.1184 Abstract | arXiv Analytics

arXiv:1206.1184 [math.DG]Abstract References Reviews Resources

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

Published 2012-06-06, updated 2015-08-06Version 3

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.

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

Journal: Journal of Differential Equations, 259 (2015) 2626-2694

DOI: 10.1016/j.jde.2015.04.011

Categories: math.DG, math.AP

Subjects: 35J65, 53C25

Keywords: scalar-flat metrics, yamabe flow, convergence, compact riemannian manifolds, yamabe-type flow

Tags: journal article

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