Analytic capacity and holomorphic motions-Reference-Cited by-同舟云学术

Analytic capacity and holomorphic motions

Published:2019-07-02 Issue:7 Volume:23 Page:130-134
ISSN:1088-4173
Container-title:Conformal Geometry and Dynamics of the American Mathematical Society
language:en
Short-container-title:Conform. Geom. Dyn.

Author:

Pouliasis Stamatis,Ransford Thomas,Younsi Malik

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.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology

Link

http://www.ams.org/ecgd/2019-23-07/S1088-4173-2019-00336-9/S1088-4173-2019-00336-9.pdf

Reference12 articles.

1. Bounded analytic functions;Ahlfors, Lars V.;Duke Math. J.,1947

2. Area distortion of quasiconformal mappings;Astala, Kari;Acta Math.,1994

3. Holomorphic motions;Astala, K.,2001

4. Universitext;Aupetit, Bernard,1991

5. Lecture Notes in Mathematics, Vol. 297;Garnett, John,1972

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Fast Computation of Analytic Capacity;Computational Methods and Function Theory;2024-06-07

2. Logarithmic capacity under holomorphic motions in higher dimensions;Journal of Mathematical Analysis and Applications;2023-11

3. Continuity of capacity of a holomorphic motion;Advances in Mathematics;2020-11

4. Continuity of condenser capacity under holomorphic motions;Canadian Mathematical Bulletin;2020-06-29