Min-max minimal hypersurface in $(M^{n+1}, g)$ with $Ric_{g}>0$ and $2\leq n\leq 6$

Xin Zhou Department of Mathematics, Stanford University

Differential Geometry mathscidoc:1610.10033

Distinguished Paper Award in 2017

Journal of Differential Geometry, 100, 129-160., 2015
In this paper, we study the shape of the min-max minimal hypersurface produced by Almgren-Pitts in F. Almgren, and J. Pitts, corresponding to the fundamental class of a Riemannian manifold $(M^{n+1}, g)$of positive Ricci curvature with 2 ≤ n ≤ 6. We characterize the Morse index, volume and multiplicity of this min-max hypersurface. In particular, we show that the min-max hypersurface is either orientable and of index one, or is a double cover of a non-orientable minimal hypersurface with least area among all closed embedded minimal hypersurfaces.
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@inproceedings{xin2015min-max,
  title={Min-max minimal hypersurface in $(M^{n+1}, g)$ with $Ric_{g}>0$ and $2\leq n\leq 6$},
  author={Xin Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010163341096077112},
  booktitle={Journal of Differential Geometry},
  volume={100},
  pages={129-160.},
  year={2015},
}
Xin Zhou. Min-max minimal hypersurface in $(M^{n+1}, g)$ with $Ric_{g}>0$ and $2\leq n\leq 6$. 2015. Vol. 100. In Journal of Differential Geometry. pp.129-160.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010163341096077112.
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