Morse index bounds for free boundary minimal hypersurfaces through covering arguments Santiago Cordero-Misteli, Stony Brook University Host: Preston Kelley This is a virtual talk. Zoom link TBA.
Abstract: How complicated can a minimal surface be? This question has led to interesting discoveries about the relationships between various notions of complexity. In this context, an important open question is the Schoen conjecture, which roughly says that the Morse index dominates the topology. This conjecture has been established in certain cases under some assumptions on the ambient curvature. In 2019, Antoine Song introduced a novel approach to prove a similar bound on the Betti numbers in terms of the Morse index. This new proof doesn't impose any ambient curvature assumptions but requires a control on the area. In this talk I will explain joint work with Giada Franz, where we generalize Song's approach to prove a similar statement for free boundary minimal hypersurfaces.
To add/edit talks, please log in on the department web page, then return to Announce. Alternatively if you know the Announce
username/password, click the link below: