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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
26/2014

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

Qi Ding, Jürgen Jost and Yuanlong Xin

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.

Received:
18.02.14
Published:
25.02.14

Related publications

inJournal
2016 Repository Open Access
Qi Ding, Jürgen Jost and Yuan-Long Xin

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

In: American journal of mathematics, 138 (2016) 2, pp. 287-327