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. 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.
Keywords:
Visible boundary, metric measure space, John domain
Affiliations des auteurs :
Ryan Gibara
1
;
Riikka Korte
2
1
University of Cincinnati, Department of Mathematical Sciences
2
Aalto University, Department of Mathematics and Systems Analysis
Ryan Gibara; Riikka Korte. Accessible parts of the boundary for domains in metric measure spaces. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 695-706. doi: 10.54330/afm.116365
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author = {Ryan Gibara and Riikka Korte},
title = {Accessible parts of the boundary for domains in metric measure spaces},
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