English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We generalize a bi-Lipschitz extension result of David and Semmes fromEuclidean spaces to complete metric measure spaces with controlled geometry(Ahlfors regularity and supporting a Poincar\'e inequality). In particular, wefind sharp conditions on metric measure spaces $X$ so that any bi-Lipschitzembedding of a subset of the real line into $X$ extends to a bi-Lipschitzembedding of the whole line. Along the way, we prove that if the complement ofan open subset $Y$ of $X$ has small Assouad dimension, then it is a uniformdomain. Finally, we prove a quantitative approximation of continua in $X$ bybi-Lipschitz curves.

Bi-Lipschitz arcs in metric spaces with controlled geometry