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Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 138, Number 2, April 2016
- pp. 287-327
- 10.1353/ajm.2016.0009
- Article
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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.