Title: The Zero Scalar Curvature Yamabe problem on noncompact manifolds with boundary

Authors: Fernando A Schwartz

Issue: Volume 55 (2006), Issue 4, 1449-1460

Abstract: Let $(M^{n},g)$, $n \ge 3$ be a noncompact complete Riemannian manifold with compact boundary and $f$ a smooth function on $\partial M$. In this paper we show that for a large class of such manifolds, there exists a metric within the conformal class of $g$ that is complete, has zero scalar curvature on $M$, and has mean curvature $f$ on the boundary. The problem is equivalent to finding a positive solution to an elliptic equation with a non-linear boundary condition with critical Sobolev exponent.