Min-Max Widths of the Unit 3-Sphere and a Strong Multiplicity One Theorem
Time: 2023-10-27
Published By: Wenqiong Li
Speaker(s): Yangyang Li (The University of Chicago)
Time: 09:00-10:00 November 1, 2023
Venue: Online
Abstract: The recent advancements in Almgren-Pitts min-max theory have revealed the abundance of minimal hypersurfaces in closed manifolds. Specifically, each min-max width can be represented by a disjoint union of minimal hypersurfaces. However, obtaining precise estimates on these widths remains a significant challenge, even in the case of the unit 3-sphere. In this talk, I will discuss a recent joint work with Adrian Chu, in which we show that the min-max 10-width to 13-width of the unit 3-sphere lie strictly between 2π^2 (the area of a Clifford torus) and 8π (twice the area of an equator). This partially answers a question posed by F. Marques and A. Neves. Our result is achieved via a strong multiplicity one theorem.
Bio-Sketch: Yangyang Li is currently a Dickson Instructor at the University of Chicago, supervised by André Neves. He received his Ph.D. in 2022 from Princeton University, advised by Fernando Codá Marques. His research interests lie in differential geometry and geometric PDEs, with a focus on geometric variational problems.
ID: 876 9745 2824 Passcode: 060811
