Morse index of multiplicity one min-max minimal hypersurfaces

Abstract

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 ( [31] , [34] , [36] , [43] ) proposed by the authors with the goal of developing a Morse theory for the area functional.