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On Frankel’s Theorem

Published online by Cambridge University Press:  20 November 2018

Peter Petersen
Affiliation:
Department of Mathematics, University of California-Los Angeles, Los Angeles, California 90095-1555, U.S.A., e-mail: [email protected]
Frederick Wilhelm
Affiliation:
Department of Mathematics, University of California-Riverside, Riverside, California 92521-0135, U.S.A., e-mail: [email protected]
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2003

References

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