Alexandrov spaces with integral current structure
Alexandrov spaces with integral current structure
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DOI：
10.4310/cag.2021.v29.n1.a4
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发表时间：
2017-03
影响因子：
0.7
通讯作者：
Maree Jaramillo;Raquel Perales;Priyanka Rajan;C. Searle;Anna Siffert
中科院分区：
文献类型：
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作者：
Maree Jaramillo;Raquel Perales;Priyanka Rajan;C. Searle;Anna Siffert
我们赋予每一个闭合的、可定向的Alexandrov空间$(X, d)$一个权为1的积分电流$T$, $\偏T = 0, $ set(T) = X$，即证明$(X, d， T)$是一个没有边界的积分电流空间。结合Li和Perales的结果，我们证明了这些具有一致下曲率和直径界的空间的非坍缩序列允许其Gromov-Hausdorff和本然平面极限一致的子序列。
We endow each closed, orientable Alexandrov space $(X, d)$ with an integral current $T$ of weight equal to 1, $\partial T = 0 and \set(T) = X$, in other words, we prove that $(X, d, T)$ is an integral current space with no boundary. Combining this result with a result of Li and Perales, we show that non-collapsing sequences of these spaces with uniform lower curvature and diameter bounds admit subsequences whose Gromov-Hausdorff and intrinsic flat limits agree.