The topology of area-minimizing surfaces in manifolds of non-negative curvature

Work of Schoen--Yau in the 70's/80's shows that area-minimizing (actually stable) two-sided surfaces in three-manifolds of non-negative scalar curvature are of a special topological type: a sphere, torus, plane or cylinder. The torus and cylinder cases are "borderline" for this estimate. It was shown by Cai--Galloway in the late 80's that the torus can only occur in a very special ambient three manifold. We complete the story by showing that a similar result holds for the cylinder. The talk should be accessible to those with a basic knowledge of curvature in Riemannian geometry.