论文标题
Geroch猜想的概括
A generalization of Geroch's conjecture
论文作者
论文摘要
帽子的定理 - 以拓扑结构$ m^{n-1} \ times \ mathbb {s}^1 $不接受积极的ricci曲率指标，而geroch的猜想的分辨率则意味着torus $ \ mathbb {t}^n $ cultrecar cult cul form culit culit culit culit culit culit culit culit cultrics cultrip cultrect cultrone。 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.
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.
