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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 287-327
Launched on MUSE
2016-04-04
Open Access
No
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