Steve Buckley:

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"Uniform domains and capacity" 

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ABSTRACT: 

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Uniform domains are in many ways the "good" domains in geometric
analysis. We discuss this important class of Euclidean domains and
characterize them in terms of conformal capacity.  Along the way, we
establish links between other classes of Euclidean domains, such as
Loewner domains, quasi-extremal distance domains, and domains in which
the quasihyperbolic metric is Gromov hyperbolic.