Blow-up phenomena for scalar-flat metrics on manifolds with boundary

Abstract

Let (M,g) be a compact n-dimensional Riemannian manifold with boundary. This article is concerned with the set of scalar-flat metrics on M which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We construct examples of metrics on the unit ball, in dimensions n>=25, for which this set is noncompact. These manifolds have umbilic boundary, but they are not conformally equivalent to the unit ball.

arXiv comment44 pages. Some typos corrected. This is a more detailed version of a paper accepted to Journal of Differential Equations

References in corpus (3)

• A compactness theorem for scalar-flat metrics on manifolds with boundary
• Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions
• An existence theorem for the Yamabe problem on manifolds with boundary

Cited by in corpus (6)

• 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
• A compactness result for scalar-flat metrics on manifolds with umbilic boundary
• The asymptotic behavior of Palais-Smale sequences on manifolds with boundary
• Linear perturbation of the Yamabe problem on manifolds with boundary
• Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation