Minimal Hypersurfaces in compact symmetric spaces

Marco Radeschi, University of Notre Dame
Fine Hall 314

A conjecture of Marquez-Neves-Schoen says that for every embedded minimal hypersurface M in a manifold of positive Ricci curvature, the first Betti number of M is bounded above linearly by the index of M. We will show that for every compact symmetric space this result holds, up to replacing the index of M with its extended index. Moreover, we provide families of examples for which the actual conjecture holds for an open set of metrics. These results are a joint work with R. Mendes and Claudio Gorodski.