Seminars

 Lecture Announcement Date: Wednesday, August 10, 2022. Time: 3:30 PM. Venue: Seminar Hall Existence of multiple closed CMC hypersurfaces with small mean curvature Akashdeep Dey University of Toronto. 10-08-22 Abstract The Almgren-Pitts min-max theory deals with the min-max construction of closed minimal hypersurfaces. By the combined works of Almgren, Pitts and Schoen-Simon, every closed Riemannian manifold (M^n , g), n \geq 3, contains at least one closed minimal hypersurface. Recently, the Almgren-Pitts min-max theory has been further developed to show that minimal hypersurfaces exist in abundance. By the works of Marques-Neves and Song, every closed Riemannian manifold (M^n , g), 3 \leq n \leq 7 contains infinitely many closed minimal hypersurfaces. This was conjectured by Yau. Min-max theory for the constant mean curvature (CMC) hypersurfaces has been recently developed by Zhou-Zhu and Zhou. In particular, Zhou and Zhu proved that for any c > 0, every closed Riemannian manifold (M^n , g), n \geq 3, contains a closed c-CMC hypersurface. In the first half of my talk I will briefly discuss the min-max theory for the minimal and CMC hypersurfaces. In the second half, I will talk about the following result. The number of closed c-CMC hypersurfaces in a closed Riemannian manifold (M^n , g), n \geq 3, tends to infinity as c tends to 0^+.