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arXiv:1011.4235 [math.DG]AbstractReferencesReviewsResources

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

Sergio Almaraz

Published 2010-11-18, updated 2011-05-04Version 2

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.

Comments: 44 pages. Some typos corrected. This is a more detailed version of a paper accepted to Journal of Differential Equations
Journal: Journal of Differential Equations, 251(7), 1813-1840 (2011)
Categories: math.DG, math.AP
Subjects: 35J65, 53C25
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