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 (, , , ) proposed by the authors with the goal of developing a Morse theory for the area functional.
All Science Journal Classification (ASJC) codes
- Min-max methods
- Minimal surfaces
- Morse Index