Uniformly Perfect Sets, Hausdorff Dimension, and Conformal Capacity
Uniformly Perfect Sets, Hausdorff Dimension, and Conformal Capacity
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 $$\mathbb {R}^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> to prove new explicit lower bounds for the Hausdorff dimension of …