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

Qi Ding; J. Jost; Y. L. Xin

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arXiv · 1308.4963

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

Qi Ding·J. Jost·Y. L. Xin

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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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BibTeX RIS

Qi Ding, J. Jost, Y. L. Xin. 2013-08-22. Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature. https://arxiv.org/abs/1308.4963

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