Doug Stryker dstryker at princeton dot edu
Stable minimal hypersurfaces in 4-manifolds
In 1982, Schoen and Yau showed that 3-manifolds with positive Ricci curvature do not admit complete stable minimal hypersurfaces. Using this fact, they showed that Euclidean space is the only noncompact 3-manifold admitting a complete metric with positive Ricci curvature. I will discuss some features of the analogous problem in 4-manifolds, based on joint work with Otis Chodosh and Chao Li. In particular, I will discuss ambient curvature conditions on 4-manifolds that prohibit complete stable minimal hypersurfaces, as well as some topological consequences of this result.