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arXiv · 1803.04273

Morse index of multiplicity one min-max minimal hypersurfaces

Fernando C. Marques·André Neves
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Abstract

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 (\cite{marques-icm}, \cite{marques-neves-cycles}, \cite{marques-neves-index}, \cite{neves-icm}) proposed by the authors with the goal of developing a Morse theory for the area functional.

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Fernando C. Marques, André Neves. 2018-03-12. Morse index of multiplicity one min-max minimal hypersurfaces. https://arxiv.org/abs/1803.04273

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