Analytic capacity and holomorphic motions

Stamatis Pouliasis, Thomas Ransford, Malik Younsi

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)130-134
Number of pages5
JournalConformal Geometry and Dynamics
Volume23
Issue number7
DOIs
StatePublished - 2019

Keywords

  • Analytic capacity
  • Harmonic function
  • Holomorphic motion

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