Recent Developments in Constant Mean Curvature Hypersurfaces

A constant mean curvature surface is a critical point of the area functional subject to a volume constraint. Min-max theory is a powerful method for finding saddle type critical points of functionals. Recently, Xin Zhou and Jonathan Zhu developed a min-max theory for finding constant mean curvature surfaces in closed manifolds. In this talk, I will discuss some recent results in the min-max theory of constant mean curvature hypersurfaces. In particular, I will discuss an extension of the CMC min-max theory to certain non-compact manifolds. I will also discuss joint work with Xin Zhou on min-max theory with a volume constraint.