On the analytic and Cauchy capacities

We give new sufficient conditions for a compact set $E \subseteq \mathbb{C}$ to satisfy $γ(E)=γ_c(E)$, where $γ$ is the analytic capacity and $γ_c$ 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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