Morse theory for the area functional
This article is a survey on the path leading to a Morse-theoretic result for the area functional in codimension one, that is, any closed manifold of low dimension endowed with a smooth metric can be approximated with smooth, closed, embedded minimal hypersurfaces satisfying some properties. After a short historic introduction, it introduces the different tools needed to prove the central result of the survey. Namely, they need upper bounds on the index, lower bounds when multiplicities are equal to one and the multiplicity one conjecture (by now, a theorem). A sketch of the proofs follows.
scientific article; zbMATH DE number 7375685
scientific article