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May 2015 Min-max minimal hypersurface in $(M^{n+1}, g)$ with $Ric \geq 0$ and $2 \leq n \leq 6$
Xin Zhou
J. Differential Geom. 100(1): 129-160 (May 2015). DOI: 10.4310/jdg/1427202766


In this paper, we study the shape of the min-max minimal hypersurface produced by Almgren-Pitts in F. Almgren, The theory of varifolds, and J. Pitts, Existence and regularity of minimal surfaces on Riemannian manifold, corresponding to the fundamental class of a Riemannian manifold $(M^{n+1}, g)$ of positive Ricci curvature with $2 \leq n \leq 6$. We characterize the Morse index, area, 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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Xin Zhou. "Min-max minimal hypersurface in $(M^{n+1}, g)$ with $Ric \geq 0$ and $2 \leq n \leq 6$." J. Differential Geom. 100 (1) 129 - 160, May 2015.


Published: May 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1331.53092
MathSciNet: MR3326576
Digital Object Identifier: 10.4310/jdg/1427202766

Rights: Copyright © 2015 Lehigh University


Vol.100 • No. 1 • May 2015
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