Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173



Analytic capacity and holomorphic motions

Authors: Stamatis Pouliasis, Thomas Ransford and Malik Younsi
Journal: Conform. Geom. Dyn. 23 (2019), 130-134
MSC (2010): Primary 30C85; Secondary 31A15, 37F99
Published electronically: July 2, 2019
MathSciNet review: 3976592
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 30C85, 31A15, 37F99

Retrieve articles in all journals with MSC (2010): 30C85, 31A15, 37F99

Additional Information

Stamatis Pouliasis
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
MR Author ID: 951898

Thomas Ransford
Affiliation: Département de mathématiques et de statistique, Université Laval, Québec (Québec), G1V 0A6, Canada
MR Author ID: 204108

Malik Younsi
Affiliation: Department of Mathematics, University of Hawaii Manoa, Honolulu, Hawaii 96822
MR Author ID: 1036614

Keywords: Analytic capacity, holomorphic motion, harmonic function
Received by editor(s): September 10, 2018
Published electronically: July 2, 2019
Additional Notes: The second author was supported by grants from NSERC and the Canada Research Chairs program.
The third author was supported by NSF Grant DMS-1758295
Article copyright: © Copyright 2019 American Mathematical Society