On the analytic and Cauchy capacities
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We give new sufficient conditions for a compact set E ⊆ C to satisfy γ(E) = γc(E), where γ is the analytic capacity and γc is the Cauchy capacity. As a consequence, we provide examples of compact plane sets such that the above equality holds but the Ahlfors function is not the Cauchy transform of any complex Borel measure supported on the set.
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