Abstract
We show that a Riemannian manifold of dimension at least 3 can be recovered from the space of boundaries of rectifiable integral 2-currents (the “lcycles”) equipped with the filling area distance, and discuss possible approaches to “spaces with area structures”.
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with appendix by Nigel Higson
The first author is partially supported by the NSF Grant DMS-0412166.
The second author is partially supported by the Dynasty foundation and RFBR grant 08-01-00079-a.
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Burago, D., Ivanov, S. Area Spaces: First Steps. Geom. Funct. Anal. 19, 662–677 (2009). https://doi.org/10.1007/s00039-009-0018-2
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DOI: https://doi.org/10.1007/s00039-009-0018-2