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