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math.CV2020★ 6 cited
Analytic capacity and holomorphic motions
Stamatis Pouliasis, Thomas Ransford, Malik Younsi
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 sho…
math.CV2020
Continuity of capacity of a holomorphic motion
Thomas Ransford, Malik Younsi, Wen-hui Ai
We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity m…