Analytic capacity and holomorphic motions

Stamatis Pouliasis; Thomas Ransford; Malik Younsi

doi:10.1090/ECGD/336

Analytic capacity and holomorphic motions

Stamatis Pouliasis, Thomas Ransford, Malik Younsi

Mathematics and Statistics

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3 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 language	English
Pages (from-to)	130-134
Number of pages	5
Journal	Conformal Geometry and Dynamics
Volume	23
Issue number	7
DOIs	https://doi.org/10.1090/ECGD/336
State	Published - 2019

Keywords

Analytic capacity
Harmonic function
Holomorphic motion

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10.1090/ECGD/336

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title = "Analytic capacity and holomorphic motions",

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.",

keywords = "Analytic capacity, Harmonic function, Holomorphic motion",

author = "Stamatis Pouliasis and Thomas Ransford and Malik Younsi",

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doi = "10.1090/ECGD/336",

language = "English",

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journal = "Conformal Geometry and Dynamics",

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AU - Pouliasis, Stamatis

AU - Ransford, Thomas

AU - Younsi, Malik

PY - 2019

Y1 - 2019

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AB - 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.

KW - Analytic capacity

KW - Harmonic function

KW - Holomorphic motion

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U2 - 10.1090/ECGD/336

DO - 10.1090/ECGD/336

M3 - Article

AN - SCOPUS:85071375748

SN - 1088-4173

VL - 23

SP - 130

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JO - Conformal Geometry and Dynamics

JF - Conformal Geometry and Dynamics

IS - 7

ER -

Analytic capacity and holomorphic motions

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Keywords

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