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arXiv:1807.08406 [math.DG]AbstractReferencesReviewsResources

A compactness theorem for scalar-flat metrics on 3-manifolds with boundary

Sergio Almaraz, Olivaine S. de Queiroz, Shaodong Wang

Published 2018-07-23Version 1

Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. This involves a blow-up analysis of a Yamabe-type equation with critical Sobolev exponent on the boundary.

Comments: 24 pages
Categories: math.DG, math.AP
Subjects: 53C21, 35J65
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