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Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature

Qi Ding Fudan University J. Jost Max Planck Institute for Mathematics in the Sciences Yuanlong Xin Fudan University

Differential Geometry mathscidoc:1912.10002

Amer. J. Math., 138, (2), 287-327, 2016
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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@inproceedings{qi2016existence,
  title={Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature},
  author={Qi Ding, J. Jost, and Yuanlong Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224114351444546022},
  booktitle={Amer. J. Math.},
  volume={138},
  number={2},
  pages={287-327},
  year={2016},
}
Qi Ding, J. Jost, and Yuanlong Xin. Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature. 2016. Vol. 138. In Amer. J. Math.. pp.287-327. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224114351444546022.
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