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arXiv · 1011.4235

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

Sergio Almaraz
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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.

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Sergio Almaraz. 2011-05-04. Blow-up phenomena for scalar-flat metrics on manifolds with boundary. https://doi.org/10.1016/j.jde.2011.04.013

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