• Corpus ID: 215814586

On the intersection of minimal hypersurfaces of $S^k$.

  title={On the intersection of minimal hypersurfaces of \$S^k\$.},
  author={Renan Assimos},
  journal={arXiv: Differential Geometry},
  • Renan Assimos
  • Published 17 April 2020
  • Mathematics
  • arXiv: Differential Geometry
It is known since the work of Frankel that two compactly immersed minimal hypersurfaces in a manifold with positive Ricci curvature must have an intersection point. Several generalizations of this result can be found in the literature, for example in the works of Lawson, Petersen and Wilhelm, among others. In the special case of minimal hypersurfaces of $S^k$, we prove a stronger version of Frankel's theorem. Namely, we show that if two compact minimal hypersurfaces $M_1$, $M_2$ of $S^k$ and a… 
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