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On Frankel’s Theorem

Published online by Cambridge University Press:  20 November 2018

Peter Petersen  and
Frederick Wilhelm
Peter Petersen
Affiliation:
Department of Mathematics, University of California-Los Angeles, Los Angeles, California 90095-1555, U.S.A., e-mail: petersen@math.ucla.edu
Frederick Wilhelm
Affiliation:
Department of Mathematics, University of California-Riverside, Riverside, California 92521-0135, U.S.A., e-mail: fred@math.ucr.edu
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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.

Keywords

53C20Frankel’s Theorem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 130 - 139
Copyright
Copyright © Canadian Mathematical Society 2003

References

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