A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Uniformly Perfect Sets, Hausdorff Dimension, and Conformal Capacity
Tekijät: Rainio Oona, Sugawa Toshiyuki, Vuorinen, Matti
Kustantaja: Springer Nature
Julkaisuvuosi: 2024
Journal: Journal of Geometric Analysis
Tietokannassa oleva lehden nimi: JOURNAL OF GEOMETRIC ANALYSIS
Artikkelin numero: ARTN 154
Vuosikerta: 34
Numero: 6
ISSN: 1050-6926
eISSN: 1559-002X
DOI: https://doi.org/10.1007/s12220-024-01599-5
Verkko-osoite: https://link.springer.com/article/10.1007/s12220-024-01599-5
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/393346031
Using the definition of uniformly perfect sets in terms of convergent sequences, we apply lower bounds for the Hausdorff content of a uniformly perfect subset E of Rn to prove new explicit lower bounds for the Hausdorff dimension of E. These results also yield lower bounds for capacity test functions, which we introduce, and enable us to characterize domains of Rn with uniformly perfect boundaries. Moreover, we show that an alternative method to define capacity test functions can be based on the Whitney decomposition of the domain considered.
Ladattava julkaisu This is an electronic reprint of the original article. |