Analytic capacity and holomorphic motions

Pouliasis, Stamatis; Ransford, Thomas; Younsi, Malik

doi:10.1090/ecgd/336

Analytic capacity and holomorphic motions
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by Stamatis Pouliasis, Thomas Ransford and Malik Younsi PDF

Conform. Geom. Dyn. 23 (2019), 130-134 Request permission

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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