Morse index of multiplicity one min-max minimal hypersurfaces
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 (marques-icm, marques-neves-cycles, marques-neves-index, neves-icm) proposed by the authors with the goal of developing a Morse theory for the area functional.
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