Alexandrov spaces with integral current structure

摘要

We endow each closed, orientable Alexandrov space (X, d) with an integral current T of weight equal to 1, partial derivative 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.