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# 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.

**Category**: Geometry and Topology**Duration**: 01:34:39**Date**: October 17, 2022 at 3:10 PM-
**Tags:**seminar, Geometry and Topology Seminar

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