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 (\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.
Cite
@article{arxiv.1803.04273,
title = {Morse index of multiplicity one min-max minimal hypersurfaces},
author = {Fernando C. Marques and André Neves},
journal= {arXiv preprint arXiv:1803.04273},
year = {2019}
}
Comments
53 pages. We have added an Addendum to reflect the solution by X. Zhou of our Multiplicity One Conjecture 1.2. We have extended our Main Theorem 1.3 to obtain, in light of Zhou's paper, the precise characterization of the Morse index of min-max minimal hypersurfaces for generic metrics. This finishes the Morse-theoretic program proposed by the authors for the area functional (Theorem 8.4)