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arXiv · 2011.11508

Analytic capacity and holomorphic motions

Stamatis Pouliasis·Thomas Ransford·Malik Younsi
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Abstract

We study the behavior of the analytic capacity of a compact set under deformations obtained by families of conformal maps depending holomorphically on the complex parameter. We show that, under those deformations, the logarithm of the analytic capacity varies harmonically. We also show that the hypotheses in this result cannot be substantially weakened.

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Stamatis Pouliasis, Thomas Ransford, Malik Younsi. 2020-11-23. Analytic capacity and holomorphic motions. https://doi.org/10.1090/ecgd%2F336

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