Geodesic
Accessible parts of the boundary for domains in metric measure spaces
Ryan Gibara1 ; Riikka Korte2
1 University of Cincinnati, Department of Mathematical Sciences
2 Aalto University, Department of Mathematics and Systems Analysis
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 695-706.

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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.  
DOI : 10.54330/afm.116365
Keywords: Visible boundary, metric measure space, John domain

Ryan Gibara 1 ; Riikka Korte 2

1 University of Cincinnati, Department of Mathematical Sciences
2 Aalto University, Department of Mathematics and Systems Analysis 
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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. http://geodesic.mathdoc.fr/articles/10.54330/afm.116365/

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