An existence theorem of conformal scalar-flat metrics on manifolds with boundary

Sérgio de Moura Almaraz

Vol. 248 (2010), No. 1, 1–22

DOI: 10.2140/pjm.2010.248.1

Abstract

Let (M,g) be a compact Riemannian manifold with boundary. We address the Yamabe-type problem of finding a conformal scalar-flat metric on M whose boundary is a constant mean curvature hypersurface. When the boundary is umbilic, we prove an existence theorem that finishes some of the remaining cases of this problem.

Keywords

Yamabe problem, manifold with boundary, scalar curvature, mean curvature, Weyl tensor

Mathematical Subject Classification 2000

Primary: 53C25

Secondary: 35J65

Milestones

Received: 4 July 2009

Accepted: 16 January 2010

Published: 1 October 2010