Accessible parts of the boundary for domains in metric measure spaces
Finna-arvio
Accessible parts of the boundary for domains in metric measure spaces
Alueen näkyvä reuna metrisissä avaruuksissa
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.
Tallennettuna:
Kieli |
englanti |
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Sarja | Annales Fennici Mathematici |
Aiheet | |
ISSN |
2737-0690 2737-114X |
DOI | 10.54330/afm.116365 |