A generalization of Geroch's conjecture
| Autor: | Brendle, Simon, Hirsch, Sven, Johne, Florian |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | The Theorem of Bonnet--Myers implies that manifolds with topology $M^{n-1} \times \mathbb{S}^1$ do not admit a metric of positive Ricci curvature, while the resolution of Geroch's conjecture implies that the torus $\mathbb{T}^n$ 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 $n \leq 7$ the manifolds $N^n = M^{n-m} \times \mathbb{T}^m$ do not admit a metric of positive $m$-intermediate curvature. Comment: final version; to appear in Comm. Pure. Appl. Math |
| Databáze: | arXiv |
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