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arXiv · 1411.7263

On the analytic and Cauchy capacities

Malik Younsi
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Abstract

We give new sufficient conditions for a compact set $E \subseteq \mathbb{C}$ to satisfy $\gamma(E)=\gamma_c(E)$, where $\gamma$ is the analytic capacity and $\gamma_c$ 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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Malik Younsi. 2014-11-26. On the analytic and Cauchy capacities. https://arxiv.org/abs/1411.7263

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