Blow-up phenomena for scalar-flat metrics on manifolds with boundary
Differential Geometry
2011-08-01 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1011.4235,
title = {Blow-up phenomena for scalar-flat metrics on manifolds with boundary},
author = {Sergio Almaraz},
journal= {arXiv preprint arXiv:1011.4235},
year = {2011}
}
Comments
44 pages. Some typos corrected. This is a more detailed version of a paper accepted to Journal of Differential Equations