Minimal hypersurfaces in a generic 8-dimensional closed Riemannian manifold
Dr. Yangyang Li
2023-06-19 9:00-10:00
MCM110&Online
Speaker: Dr. Yangyang Li (Chicago University)Time: 9:00-10:00 June 19, 2023 (Monday)
Place: MCM110 & Online (Zoom ID: 3329836068 Password: mcm1234)
Title: Minimal hypersurfaces in a generic 8-dimensional closed Riemannian manifold
Abstract: In the past decade, the Almgren-Pitts min-max theory has advanced the theory of minimal hypersurfaces in a closed Riemannian manifold (M^{n+1}, g). Extensive research has been conducted on various properties of these minimal hypersurfaces, such as areas, Morse indices, multiplicities, and spatial distributions, when 3 ≤ n+1 ≤ 7. However, in higher dimensions, singularities may arise in the constructed minimal hypersurfaces. This occurrence invalidates many techniques that are effective in the low dimensions when investigating these geometric objects. In this talk, I will discuss how to overcome this difficulty in a generic 8-dimensional closed manifold, employing various deformation arguments. En route to obtaining generic results, we establish the generic regularity of minimal hypersurfaces in dimension 8. The talk is based on joint works with Zhihan Wang.
