Morse index of multiplicity one min-max minimal hypersurfaces

In this paper, we prove that the Morse index of a multiplicity one, smooth, min-max minimal hypersurface is generically equal to the dimension of the homology class detected by the families used in the construction. This confirms part of the program ([31], [34], [36], [43]) proposed by the authors w...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2021-02, Vol.378, p.107527, Article 107527
Main Authors: Marques, Fernando C., Neves, André
Format: Article
Language:English
Subjects:
Min-max methods
Minimal surfaces
Morse Index
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Summary:In this paper, we prove that the Morse index of a multiplicity one, smooth, min-max minimal hypersurface is generically equal to the dimension of the homology class detected by the families used in the construction. This confirms part of the program ([31], [34], [36], [43]) proposed by the authors with the goal of developing a Morse theory for the area functional.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2020.107527