Mean curvature in manifolds with Ricci curvature bounded from below
Jaigyoung Choe
Korea Institute for Advanced Study (KIAS), Seoul, Republic of KoreaAilana Fraser
The University of British Columbia, Vancouver, Canada
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Abstract
Let be a compact Riemannian manifold of nonnegative Ricci curvature and a compact embedded 2-sided minimal hypersurface in . It is proved that there is a dichotomy: If does not separate then is totally geodesic and is isometric to the Riemannian product , and if separates then the map induced by inclusion is surjective. This surjectivity is also proved for a compact 2-sided hypersurface with mean curvature in a manifold of Ricci curvature Ric, , and for a free boundary minimal hypersurface in an -dimensional manifold of nonnegative Ricci curvature with nonempty strictly convex boundary. As an application it is shown that a compact -dimensional manifold with the number of generators of cannot be minimally embedded in the flat torus .
Cite this article
Jaigyoung Choe, Ailana Fraser, Mean curvature in manifolds with Ricci curvature bounded from below. Comment. Math. Helv. 93 (2018), no. 1, pp. 55–69
DOI 10.4171/CMH/429