Topology and geometry of metrics of positive intermediate curvature
ABSTRACT
The notion of m-intermediate curvature interpolates between Ricci curvature and scalar curvature. In this talk we describe extentions of classical results by Bonnet--Myers and Schoen--Yau to the setting of $m$-intermediate curvature: A non-existence result for metrics of positive m-intermediate curvature on manifolds with topology $N^n = \mathbb{T}^m \times \mathbb{S}^{n-m}$; a gluing result for manifolds with $m$-convex boundary; inheritance of spectral positivity along stable minimal hypersurfaces, and estimates for the $m$-diameter for uniform positive lower bounds.
This talk is partially based on joint work with Simon Brendle and Sven Hirsch, and joint work with Aaron Chow and Jingbo Wan.