Accessible parts of the boundary for domains in metric measure spaces

Ryan Gibara*, Riikka Korte

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

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 ≤ Q − 1. The visible boundary is the set of points that can be reached by a John curve from a fixed point z0∈Ω. This generalizes recent results by Koskela–Nandi–Nicolau (from R2) and Azzam (Rn). In particular, our approach shows that the phenomenon is independent of the linear structure of the space.

Translated title of the contributionAlueen näkyvä reuna metrisissä avaruuksissa
Original languageEnglish
Pages (from-to)695-706
Number of pages12
JournalAnnales Fennici Mathematici
Volume47
Issue number2
DOIs
Publication statusPublished - 2022
MoE publication typeA1 Journal article-refereed

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