A generalization of Geroch's conjecture

The Theorem of Bonnet–Myers implies that manifolds with topology do not admit a metric of positive Ricci curvature, while the resolution of Geroch's conjecture implies that the torus does not admit a metric of positive scalar curvature. In this work we introduce a new notion of curvature interpolating between Ricci and scalar curvature (so‐called m ‐intermediate curvature), and use stable weighted slicings to show that for and the manifolds do not admit a metric of positive m ‐intermediate curvature.