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Abstract
We prove in the setting of QAhlfors regular PIspaces the following result: if a domain has uniformly large boundary when measured with respect to the sdimensional Hausdorff content, then its visible boundary has large tdimensional 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 R^{2}) and Azzam (R^{n}). In particular, our approach shows that the phenomenon is independent of the linear structure of the space.
Translated title of the contribution  Alueen näkyvä reuna metrisissä avaruuksissa 

Original language  English 
Pages (fromto)  695706 
Number of pages  12 
Journal  Annales Fennici Mathematici 
Volume  47 
Issue number  2 
DOIs  
Publication status  Published  2022 
MoE publication type  A1 Journal articlerefereed 
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Dive into the research topics of 'Accessible parts of the boundary for domains in metric measure spaces'. Together they form a unique fingerprint.Projects
 1 Finished

Parabolic flows with variational methods
Korte, R., Evdoridis, S., Vestberg, M., Buffa, V., Myyryläinen, K., Kurki, E., Pacchiano Camacho, C., Takala, T. & Weigt, J.
01/09/2017 → 31/08/2021
Project: Academy of Finland: Other research funding