Horizons in noncompact fill-ins of nonnegative scalar curvature

Abstract

Given a complete Riemannian metric of nonnegative scalar curvature on $\Sigma \times (-\infty ,0]$, where $\Sigma$ denotes a $2$-sphere, we exhibit conditions that imply the existence of a closed minimal surface homologous to the boundary.

9 pages. Revised following peer review; several arguments and parts of the exposition have been improved. Version corresponding to the published article