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On Frankel's Theorem

Published:2003-03-01
Printed: Mar 2003
• Peter Petersen
• Frederick Wilhelm
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Abstract

In this paper we show that two minimal hypersurfaces in a manifold with positive Ricci curvature must intersect. This is then generalized to show that in manifolds with positive Ricci curvature in the integral sense two minimal hypersurfaces must be close to each other. We also show what happens if a manifold with nonnegative Ricci curvature admits two nonintersecting minimal hypersurfaces.
 Keywords: Frankel's Theorem Frankel's Theorem
 MSC Classifications: 53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]