Menger curvatures and $C^{1,α}$ rectifiability of measures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866914859669520384 |
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| author | Ghinassi, Silvia Goering, Max |
| author_facet | Ghinassi, Silvia Goering, Max |
| contents | We further develop the relationship between $β$-numbers and discrete curvatures to provide a new proof that under weak density assumptions, finiteness of the pointwise discrete curvature $\operatorname{curv}^α_{μ;2}(x,r)$ at $μ$- a.e. $x \in \mathbb{R}^{m}$ implies that $μ$ is $C^{1,α}$ $n$-rectifiable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_11471 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Menger curvatures and $C^{1,α}$ rectifiability of measures Ghinassi, Silvia Goering, Max Metric Geometry Classical Analysis and ODEs 28A75, 28A12 We further develop the relationship between $β$-numbers and discrete curvatures to provide a new proof that under weak density assumptions, finiteness of the pointwise discrete curvature $\operatorname{curv}^α_{μ;2}(x,r)$ at $μ$- a.e. $x \in \mathbb{R}^{m}$ implies that $μ$ is $C^{1,α}$ $n$-rectifiable. |
| title | Menger curvatures and $C^{1,α}$ rectifiability of measures |
| topic | Metric Geometry Classical Analysis and ODEs 28A75, 28A12 |
| url | https://arxiv.org/abs/1908.11471 |