论文标题
Riemannian指标空间的$ l^2 $ - cat $（0）$：较短的证明
The $L^2$-completion of the space of Riemannian metrics is CAT$(0)$: a shorter proof
论文作者
论文摘要
我们以一种更简单的方式来谴责布莱恩·克拉克（Brian Clarke）的结果：相对于$ l^2 $ distance的riemannian指标的完成空间是cat $（0）$。特别是我们表明，此完成是从标准概率空间到固定CAT $（0）$空间的$ l^2 $图的均值。
We reprove in an easier way a result of Brian Clarke: the completion of the space of Riemannian metrics of a compact, orientable smooth manifold with respect to the $L^2$-distance is CAT$(0)$. In particular we show that this completion is isometric to the space of $L^2$-maps from a standard probability space to a fixed CAT$(0)$ space.
