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Using the definition of uniformly perfect sets in terms of convergentsequences, we apply lower bounds for the Hausdorff content of a uniformlyperfect subset $E$ of $\mathbb{R}^n$ to prove new explicit lower bounds for theHausdorff dimension of $E.$ These results also yield lower bounds for capacitytest functions, which we introduce, and enable us to characterize domains of$\mathbb{R}^n$ with uniformly perfect boundaries. Moreover, we show that analternative method to define capacity test functions can be based on theWhitney decomposition of the domain considered.

Uniformly perfect sets, Hausdorff dimension, and conformal capacity