We will discuss recent results concerning bubbling analysis and index estimates for minimal hypersurfaces in Riemannian manifolds.
The existence theory guarantees that minimal hypersurfaces exist (Almgren, Pitts, Schoen-Simon) and in most cases that they exist in abundance (Marques-Neves, Marques-Neves-Irie). The results presented here are geared towards understanding the relationship between the Morse index and other geometric-analytic qualities of minimal hypersurfaces (topology, diffeomorphism type, total curvature).
This will contain joint works with Ambrozio, Carlotto and Buzano.
