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Characterizations of rectifiable metric measure spaces
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Bate, David and Li, Sean (2016) Characterizations of rectifiable metric measure spaces. Annales Scientifiques de l'Ecole Normale Superieure, 50 (1). pp. 1-37. doi:10.24033/asens.2314
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Official URL: https://doi.org/10.24033/asens.2314
Abstract
We characterize n-rectifiable metric measure spaces as those spaces that admit a countable Borel decomposition so that each piece has positive and finite n-densities and one of the following : is an n-dimensional Lipschitz differentiability space ; has n-independent Alberti representations ; satisfies David's condition for an n-dimensional chart. The key tool is an iterative grid construction which allows us to show that the image of a ball with a high density of curves from the Alberti representations under a chart map contains a large portion of a uniformly large ball and hence satisfies David's condition. This allows us to apply modified versions of previously known ‘biLipschitz pieces' results on the charts.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Journal or Publication Title: | Annales Scientifiques de l'Ecole Normale Superieure | ||||||
| Publisher: | Societe Mathematique de France | ||||||
| ISSN: | 0012-9593 | ||||||
| Official Date: | 2016 | ||||||
| Dates: |
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| Volume: | 50 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 1-37 | ||||||
| DOI: | 10.24033/asens.2314 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Open Access Version: |
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