Decomposition of integral metric currents
Metric Geometry
2021-04-16 v1 Functional Analysis
Abstract
In the setting of complete metric spaces, we prove that integral currents can be decomposed as a sum of indecomposable components. In the special case of one-dimensional integral currents, we also show that the indecomposable ones are exactly those associated with injective Lipschitz curves or injective Lipschitz loops, therefore extending Federer's characterisation to metric spaces. Moreover, some applications of our main results will be discussed.
Keywords
Cite
@article{arxiv.2104.07593,
title = {Decomposition of integral metric currents},
author = {Paolo Bonicatto and Giacomo Del Nin and Enrico Pasqualetto},
journal= {arXiv preprint arXiv:2104.07593},
year = {2021}
}
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20 pages