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Uniformly Perfect Sets, Hausdorff Dimension, and Conformal Capacity




TekijätRainio Oona, Sugawa Toshiyuki, Vuorinen, Matti

KustantajaSpringer Nature

Julkaisuvuosi2024

JournalJournal of Geometric Analysis

Tietokannassa oleva lehden nimiJOURNAL OF GEOMETRIC ANALYSIS

Artikkelin numeroARTN 154

Vuosikerta34

Numero6

ISSN1050-6926

eISSN1559-002X

DOIhttps://doi.org/10.1007/s12220-024-01599-5

Verkko-osoitehttps://link.springer.com/article/10.1007/s12220-024-01599-5

Rinnakkaistallenteen osoitehttps://research.utu.fi/converis/portal/detail/Publication/393346031


Tiivistelmä

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

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Last updated on 2024-26-11 at 14:12