Free boundary minimal hypersurfaces with least area

In this talk, I will present a joint work with Q. Guang and X. Zhou where we prove the existence of least area free boundary minimal hypersurfaces in compact manifolds with boundary. Moreover, we characterize the orientation and index of such minimal hypersurface. As a consequence, it is exactly the min-max one corresponding to the fundamental class if the ambient manifold has non-negative Ricci curvature and convex boundary.