Abstract
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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Younsi, M. On the analytic and Cauchy capacities. JAMA 135, 185–202 (2018). https://doi.org/10.1007/s11854-018-0028-9
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DOI: https://doi.org/10.1007/s11854-018-0028-9