论文标题
具有任意末端的Geroch猜想的概括
A Generalization of the Geroch Conjecture with Arbitrary Ends
论文作者
论文摘要
使用$μ$ bubbles，我们证明，对于$ 3 \ le n \ le 7 $，带有任意流形的Schoen-yau-schick $ n $ n $ n $ manifold的连接总和不承认正量表曲率的完全度量。 当要么$ 3 \ le n \ le 5 $，$ 1 \ le m \ le n-1 $或$ 6 \ le n \ le 7 $，$ m \ in \ {1，n-2，n-1 \} $中正$ m $ - 间隔曲率。这里$ M $ - 间隔曲率是Brendle，Hirsch和Johne在RICCI和标量曲率之间插值引入的新曲率概念。
Using $μ$-bubbles, we prove that for $3 \le n \le 7$, the connected sum of a Schoen-Yau-Schick $n$-manifold with an arbitrary manifold does not admit a complete metric of positive scalar curvature. When either $3 \le n \le 5$, $1 \le m \le n-1$ or $6 \le n \le 7$, $m \in \{1, n-2, n-1\}$, we also show the connected sum $(M^{n-m}\times \mathbb{T}^m) \# X^n$ where $X$ is an arbitrary manifold does not admit a metric of positive $m$-intermediate curvature. Here $m$-intermediate curvature is a new notion of curvature introduced by Brendle, Hirsch and Johne interpolating between Ricci and scalar curvature.
