Embeddedness of least area minimal hypersurfaces

  title={Embeddedness of least area minimal hypersurfaces},
  author={Antoine Song},
  journal={Journal of Differential Geometry},
  • A. Song
  • Published 9 November 2015
  • Mathematics
  • Journal of Differential Geometry
E. Calabi and J. Cao showed that a closed geodesic of least length in a two-sphere with nonnegative curvature is always simple. Using min-max theory, we prove that for some higher dimensions, this result holds without assumptions on the curvature. More precisely, in a closed $(n+1)$-manifold with $2 \leq n \leq 6$, a least area closed minimal hypersurface exists and any such hypersurface is embedded. As an application, we give a short proof of the fact that if a closed three-manifold $M$ has… 

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