A1 Refereed original research article in a scientific journal

Uniformly Perfect Sets, Hausdorff Dimension, and Conformal Capacity




AuthorsRainio Oona, Sugawa Toshiyuki, Vuorinen, Matti

PublisherSpringer Nature

Publication year2024

JournalJournal of Geometric Analysis

Journal name in sourceJOURNAL OF GEOMETRIC ANALYSIS

Article numberARTN 154

Volume34

Issue6

ISSN1050-6926

eISSN1559-002X

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

Web address https://link.springer.com/article/10.1007/s12220-024-01599-5

Self-archived copy’s web addresshttps://research.utu.fi/converis/portal/detail/Publication/393346031


Abstract

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.


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