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arXiv · 1807.08406

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

Sergio Almaraz·Olivaine S. de Queiroz·Shaodong Wang
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Abstract

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.

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Sergio Almaraz, Olivaine S. de Queiroz, Shaodong Wang. 2018-07-23. A compactness theorem for scalar-flat metrics on 3-manifolds with boundary. https://doi.org/10.1016/j.jfa.2019.01.001

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