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arXiv · 1703.08195

Alexandrov Spaces with Integral Current Structure

Maree Jaramillo·Raquel Perales·Priyanka Rajan·Catherine Searle·Anna Siffert
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Abstract

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.

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Maree Jaramillo, Raquel Perales, Priyanka Rajan, Catherine Searle, Anna Siffert. 2017-03-23. Alexandrov Spaces with Integral Current Structure. https://arxiv.org/abs/1703.08195

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