Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature
Qi Ding, Jürgen Jost,and Yuanlong Xin
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Submission date: 18. Feb. 2014
published in: American journal of mathematics, 138 (2016) 2, p. 287-327
DOI number (of the published article): 10.1353/ajm.2016.0009
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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.