Small constant uniform rectifiability
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910347099635712 |
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| author | Jeznach, Cole |
| author_facet | Jeznach, Cole |
| contents | We provide several equivalent characterizations of locally flat, $d$-Ahlfors regular, uniformly rectifiable sets $E$ in $\mathbb{R}^n$ with density close to $1$ for any dimension $d \in \mathbb{N}$ with $1 \le d \le n-1$. In particular, we show that when $E$ is Reifenberg flat with small constant and has Ahlfors regularity constant close to $1$, then the Tolsa alpha coefficients associated to $E$ satisfy a small constant Carleson measure estimate. This estimate is new, even when $d = n-1$, and gives a new characterization of chord-arc domains with small constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16858 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Small constant uniform rectifiability Jeznach, Cole Classical Analysis and ODEs 28A75 (Primary) We provide several equivalent characterizations of locally flat, $d$-Ahlfors regular, uniformly rectifiable sets $E$ in $\mathbb{R}^n$ with density close to $1$ for any dimension $d \in \mathbb{N}$ with $1 \le d \le n-1$. In particular, we show that when $E$ is Reifenberg flat with small constant and has Ahlfors regularity constant close to $1$, then the Tolsa alpha coefficients associated to $E$ satisfy a small constant Carleson measure estimate. This estimate is new, even when $d = n-1$, and gives a new characterization of chord-arc domains with small constant. |
| title | Small constant uniform rectifiability |
| topic | Classical Analysis and ODEs 28A75 (Primary) |
| url | https://arxiv.org/abs/2307.16858 |