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MiS Preprint
26/2014
Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature
Qi Ding, Jürgen Jost and Yuanlong Xin
Abstract
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.
