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

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.

arXiv comment49 pages. Final version, to appear in Calc. Var. Partial Differential Equations

References in corpus (3)

• Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions
• Blow-up phenomena for the Yamabe equation
• An existence theorem for the Yamabe problem on manifolds with boundary

Cited by in corpus (8)

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• Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow
• A compactness theorem for scalar-flat metrics on 3-manifolds with boundary
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• Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric
• A compactness result for scalar-flat metrics on manifolds with umbilic boundary
• Some a priori estimates for a critical Schrodinger-Newton equation
• Linear perturbation of the Yamabe problem on manifolds with boundary