A non-injective Assouad-type theorem with sharp dimension
| Autor: | David, Guy C. |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Lipschitz light maps, defined by Cheeger and Kleiner, are a class of non-injective "foldings" between metric spaces that preserve some geometric information. We prove that if a metric space $(X,d)$ has Nagata dimension $n$, then its "snowflakes" $(X,d^\epsilon)$ admit Lipschitz light maps to $\mathbb{R}^n$ for all $0<\epsilon<1$. This can be seen as an analog of a well-known theorem of Assouad. We also provide an application to a new variant of conformal dimension. Comment: 17 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|