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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Almaraz, Sergio de Moura

关键词: Yamabe problem;    Manifold with boundary;    Conformal metric;    Scalar curvature;    Mean curvature;   

DOI  :  10.1016/j.jde.2011.04.013

来源: Elsevier

【 摘 要 】

Let (M-n, g) be a compact Riemannian manifold with boundary partial derivative M. This article is concerned with the set of scalar-flat metrics on M which are in the conformal class of g and have partial derivative M as a constant mean curvature hypersurface. We construct examples of metrics on the unit ball B-n, in dimensions n >= 25, for which this set is non-compact. These manifolds have umbilic boundary, but they are not conformally equivalent to B-n. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free