Min-max Minimal Hypersurfaces with Higher Multiplicity

Explore a 53-minute lecture from the General Relativity Workshop where Cornell University's Xin Zhou delves into the intricacies of min-max minimal hypersurfaces with higher multiplicity. Learn about the Almgren-Pitts min-max theory and how minimal hypersurfaces are counted with integer multiplicities, with special focus on bumpy metrics where multiplicities are one due to the Marques-Neves Multiplicity One Conjecture. Discover groundbreaking research conducted jointly with Zhichao Wang (UBC) that presents the first examples of non-bumpy metrics on the standard (n+1)-sphere where the min-max theory necessarily produces higher multiplicity minimal hypersurfaces, specifically examining cases where the min-max varifold associated with the second volume spectrum is a multiplicity two n-sphere.