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Condenser capacity, exponential Blaschke products and universal covering maps


Authors: Javad Mashreghi and Stamatis Pouliasis
Journal: Proc. Amer. Math. Soc. 143 (2015), 3547-3559
MSC (2010): Primary 30C85, 30J10, 30C80, 31A15
DOI: https://doi.org/10.1090/S0002-9939-2015-12516-6
Published electronically: March 19, 2015
MathSciNet review: 3348796
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Abstract: Let $ B$ be an exponential Blaschke product, let $ C$ be a compact subset of the unit disc $ \mathbb{D}$ with positive logarithmic capacity and let $ K_{n}=B^{-1}(C)\cap \{z\in \mathbb{D}:\vert z\vert\leq 1-2^{-n}\}$. We give a sharp estimate for the rate of growth of the capacity of the condensers $ (\mathbb{D},K_{n})$. Also, we examine a similar problem for universal covering maps of multiply connected Greenian domains and we give a precise formula in the case of doubly connected domains.


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Additional Information

Javad Mashreghi
Affiliation: Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada, G1V 0A6
Email: javad.mashreghi@mat.ulaval.ca

Stamatis Pouliasis
Affiliation: Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada, G1V 0A6
Email: stamatis.pouliasis.1@ulaval.ca

DOI: https://doi.org/10.1090/S0002-9939-2015-12516-6
Keywords: Condenser capacity, Lindel\"of Principle, exponential Blaschke products, universal covering maps.
Received by editor(s): October 11, 2013
Received by editor(s) in revised form: March 17, 2014
Published electronically: March 19, 2015
Additional Notes: This work was supported by grants from NSERC (Canada) and FRQNT (Québec).
Communicated by: Pamela Gorkin
Article copyright: © Copyright 2015 American Mathematical Society