Ben Sharp

Bubbling and multiplicity analysis for CMC hypersurfaces

We will discuss some geometric and topological properties of compact CMC (constant mean curvature) hypersurfaces inside Riemannian manifolds by analysing degenerating sequences. In particular this will provide qualitative relationships between the topological, geometrical and analytical properties of these objects. Results of this form are well known for minimal hypersurfaces (when the mean curvature vanishes), but have a very different flavour when one restricts to a class with non-vanishing constant mean curvature: in particular one has a far more restrictive picture near degenerate points in the latter scenario. I will give a brief overview of what is known in the minimal setting (which includes joint works with Ambrozio, Buzano, Carlotto) and then go on to discuss a work in progress with Bourni-Tinaglia for (nonzero-)CMC hypersurfaces.