Quantitative visibility estimates for unrectifiable sets in the plane
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2013
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913241746112512 |
|---|---|
| author | Bond, M. Laba, I. Zahl, J. |
| author_facet | Bond, M. Laba, I. Zahl, J. |
| contents | The "visibility" of a planar set $S$ from a point $a$ is defined as the normalized size of the radial projection of $S$ from $a$ to the unit circle centered at $a$. Simon and Solomyak (Real Anal. Exchange 2006/07) proved that unrectifiable self-similar one-sets are invisible from every point in the plane. We quantify this by giving an upper bound on the visibility of $δ$-neighbourhoods of such sets. We also prove lower bounds on the visibility of $δ$-neighborhoods of more general sets, based in part on Bourgain's discretized sum-product estimates |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1306_5469 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Quantitative visibility estimates for unrectifiable sets in the plane Bond, M. Laba, I. Zahl, J. Classical Analysis and ODEs Metric Geometry The "visibility" of a planar set $S$ from a point $a$ is defined as the normalized size of the radial projection of $S$ from $a$ to the unit circle centered at $a$. Simon and Solomyak (Real Anal. Exchange 2006/07) proved that unrectifiable self-similar one-sets are invisible from every point in the plane. We quantify this by giving an upper bound on the visibility of $δ$-neighbourhoods of such sets. We also prove lower bounds on the visibility of $δ$-neighborhoods of more general sets, based in part on Bourgain's discretized sum-product estimates |
| title | Quantitative visibility estimates for unrectifiable sets in the plane |
| topic | Classical Analysis and ODEs Metric Geometry |
| url | https://arxiv.org/abs/1306.5469 |