Alexandrov Spaces with Integral Current Structure

Abstract

We endow each closed, orientable Alexandrov space $(X,d)$ with an integral current $T$ of weight equal to 1, $\partial T=0and\{(\}T)=X$, 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.

22 pages