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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove the quantitative equivalence of two important geometricalconditions, pertaining to the regularity of a domain$\Omega\subset\mathbb{R}^N$. These are: (i) the uniform two-sided supportingsphere condition, and (ii) the Lipschitz continuity of the outward unit normalvector. In particular, the answer to the question posed in our title is: "Thosedomains, whose unit normal is well defined and has Lipschitz constant one." Wealso offer an extension to infinitely dimensional spaces $L^p$, $p\in(1,\infty)$.

Which domains have two-sided supporting unit spheres at every boundary point?