A compactness theorem for scalar-flat metrics on manifolds with boundary
Differential Geometry
2011-05-24 v3 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.0906.0927,
title = {A compactness theorem for scalar-flat metrics on manifolds with boundary},
author = {Sergio Almaraz},
journal= {arXiv preprint arXiv:0906.0927},
year = {2011}
}
Comments
49 pages. Final version, to appear in Calc. Var. Partial Differential Equations