Intermediate curvature and a generalization of Geroch's conjecture

Florian Johne (Columbia University, New York)

Jul 04. 2023, 14:00 — 14:50

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.

A joint seminar of the Gravitational Physics Group, the Vienna Geometric Analysis Seminar and the ESI programme "Spectral theory and mathematical relativity".

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)