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

Contact the author: Please use for correspondence this email.
Submission date: 18. Feb. 2014
Pages: 33
published in: American journal of mathematics, 138 (2016) 2, p. 287-327 
DOI number (of the published article): 10.1353/ajm.2016.0009
Bibtex
Download full preprint: PDF (492 kB)

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.

07.10.2017, 01:42