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arXiv · 0906.0927

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

Sergio Almaraz
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Abstract

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.

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Sergio Almaraz. 2009-06-04. A compactness theorem for scalar-flat metrics on manifolds with boundary. https://doi.org/10.1007/s00526-010-0365-8

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