MIN-MAX MINIMAL HYPERSURFACE

被引：0
|
作者：
Zhou, Xin [1 ]
机构：
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
来源：
JOURNAL OF DIFFERENTIAL GEOMETRY | 2015年 / 100卷 / 01期
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D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the shape of the min-max minimal hypersurface produced by Almgren-Pitts in [AF2, P] corresponding to the fundamental class of a Riemannian manifold (Mn+1, g) of positive Ricci curvature with 2 <= n <= 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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页码：129 / 160
页数：32
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