On the prescribed scalar curvature problem on the three-dimensional half sphere

Mohamed Ben Ayed and Hichem Chtioui

Vol. 221 (2005), No. 2, 201–226

DOI: 10.2140/pjm.2005.221.201

Abstract

We provide a variety of classes of functions that can be realized as the scalar curvature of the standard three-dimensional half sphere with respect to some metric whose boundary mean curvature is zero. Such a problem is nontrivial, since we have to overcome topological obstructions.

Keywords

scalar curvature problem, variational problem, lack of compactness, critical points at infinity, 3D half-sphere

Mathematical Subject Classification 2000

Primary: 36J60, 35J65, 58E05

Milestones

Received: 11 August 2003

Revised: 27 October 2004

Accepted: 2 March 2005

Published: 1 October 2005