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 with the goal of developing a Morse theory for the area functional. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper demonstrates that the Morse index of a smooth, multiplicity one, min-max minimal hypersurface is typically equal to the dimension of the homology class detected by the families involved in its construction, confirming part of the authors' program for developing a Morse theory for the area functional.