• Speaker: Liam Mazurowski
• Time: 9:30-10:30
• Abstract: The solution to the isoperimetric problem shows that any closed manifold M contains a constant mean curvature hypersurface that encloses half the volume of M. This surface is obtained by minimizing area with a volume constraint. In this talk, we will investigate the existence of saddle type critical points for the area functional with half-volume constraint. First, we define the half-volume spectrum of a manifold. Then we explain how both the Allen-Cahn and Almgren-Pitts min-max theories can be used to construct surfaces achieving the half-volume spectrum. This is joint work with Xin Zhou.