论文标题
Yamabe在渐近的欧几里得歧管上，具有非阳性Yamabe常数
The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant
论文作者
论文摘要
我们研究了Yamabe在渐近平坦的歧管上的流量，并具有非阳性Yamabe常数$ y \ leq 0 $。第二名和第三名作者的先前工作\ cite \ cite {chenwang}表明，虽然yamabe流总是在$ y> 0 $时以全球加权意义收敛，但当$ y \ y \ leq 0 $时，流动必须散开。我们在此处显示在$ y \ leq 0 $案例中，但是，在适当的重新分组之后，从任何渐近平坦的歧管开始的Yamabe流都必须收敛到独特的正函数，该功能解决了原始歧管的紧凑型Yamabe问题。
We study the Yamabe flow on asymptotically flat manifolds with non-positive Yamabe constant $Y\leq 0$. Previous work by the second and third named authors \cite{ChenWang} showed that while the Yamabe flow always converges in a global weighted sense when $Y>0$, the flow must diverge when $Y\leq 0$. We show here in the $Y\leq 0$ case however that after suitable rescalings, the Yamabe flow starting from any asymptotically flat manifold must converge to the unique positive function which solves the Yamabe problem on a compactification of the original manifold.
