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

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

2009-06-04

arxiv.org/abs/0906.0927v3

Calc. Var. Partial Differential Equations 41(3), 341-386 (2011)

Mathematics

Differential Geometry

49 pages. Final version, to appear in Calc. Var. Partial Differential Equations

Scientific paper

10.1007/s00526-010-0365-8

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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