Alexandrov spaces with integral current structure

Jaramillo, Maree; Perales, Raquel; Rajan, Priyanka; Searle, Catherine; Siffert, Anna

doi:10.4310/CAG.2021.v29.n1.a4

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Journal Article

Alexandrov spaces with integral current structure

MPS-Authors

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Rajan, Priyanka
Max Planck Institute for Mathematics, Max Planck Society;

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Siffert, Anna
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://dx.doi.org/10.4310/CAG.2021.v29.n1.a4
(Publisher version)

https://doi.org/10.48550/arXiv.1703.08195
(Preprint)

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Citation

Jaramillo, M., Perales, R., Rajan, P., Searle, C., & Siffert, A. (2021). Alexandrov spaces with integral current structure. Communications in analysis and geometry, 29(1), 115-149. doi:10.4310/CAG.2021.v29.n1.a4.

Cite as: https://hdl.handle.net/21.11116/0000-0008-4715-1

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.