TY - JOUR
AU - Gibara, Ryan
AU - Korte, Riikka
PY - 2022/04/20
Y2 - 2024/10/06
TI - Accessible parts of the boundary for domains in metric measure spaces
JF - Annales Fennici Mathematici
JA - Ann. Fenn. Math.
VL - 47
IS - 2
SE - Articles
DO - 10.54330/afm.116365
UR - https://afm.journal.fi/article/view/116365
SP - 695-706
AB - <pre>We prove in the setting of \(Q\)-Ahlfors regular PI-spaces the following result: if a domain has uniformly large boundary when measured with respect to the \(s\)-dimensional Hausdorff content, then its visible boundary has large \(t\)-dimensional Hausdorff content for every \(0<t<s\leq Q-1\). The visible boundary is the set of points that can be reached by a John curve from a fixed point \(z_{0}\in \Omega\). This generalizes recent results by Koskela-Nandi-Nicolau (from \(\mathbb R^2\)) and Azzam (\(\mathbb R^n\)). In particular, our approach shows that the phenomenon is independent of the linear structure of the space.</pre><p> </p>
ER -