Intermediate curvature and a generalization of Geroch’s conjecture

Geometric Analysis and Application
Event time: 
Friday, March 3, 2023 - 2:00pm
LOM 215
Florian Johne
Speaker affiliation: 
Columbia University
Event description: 

In this talk we explain a non-existence result for metrics of positive m-intermediate curvature (a notion of curvature reducing to positive Ricci curvature for m =  1, and positive scalar curvature for m = n-1) on closed orientable manifolds with topology $N^n = M^{n-m} x \mathbb{T}^m$ for $n \leq 7$. Our proof uses a slicing constructed by minimization of weighted areas, the associated stability inequality, and estimates on the gradients of the weights and the second fundamental form of the slices. This is joint work with Simon Brendle and Sven Hirsch.