EXISTENCE AND NON-EXISTENCE OF AREA-MINIMIZING HYPERSURFACES IN MANIFOLDS OF NON-NEGATIVE RICCI CURVATURE

摘要

We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete area minimizing hypersurfaces exist. Below this value, in contrast, we construct examples.