Geometry/topology Seminar
Monday, October 17, 2022, 3:15pm, Physics 119
Florian Johne (Columbia University, Mathematics)
A generalization of Geroch's conjecture

Abstract:

Closed manifolds with topology N = M x S^1 do not admit metrics of positive Ricci curvature by the theorem of Bonnet-Myers, while the resolution of the Geroch conjecture implies that the torus T^n does not admit a metric of positive scalar curvature. In this talk we explain a non-existence result for metrics of positive m-intermediate curvature (a notion of curvature reducing to Ricci curvature for m = 1, and scalar curvature for m = n-1) on closed manifolds with topology N^n = M^{n-m} x T^m for n <= 7. Our proof uses minimization of weighted areas, the associated stability inequality, and delicate estimates on the second fundamental form. This is joint work with Simon Brendle and Sven Hirsch. [video]

---

Generated at 2:49am Wednesday, April 24, 2024 by Mcal.   Top * Reload * Login