Javascript must be enabled

Florian Johne : A generalization of Gerochs conjecture

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.

Please select playlist name from following

Report Video

Please select the category that most closely reflects your concern about the video, so that we can review it and determine whether it violates our Community Guidelines or isn’t appropriate for all viewers. Abusing this feature is also a violation of the Community Guidelines, so don’t do it.


Comments Disabled For This Video