On the asymptotic behavior of condenser capacity under Blaschke products and universal covering maps
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- by Dimitrios Betsakos, Georgios Kelgiannis, Maria Kourou and Stamatis Pouliasis PDF
- Proc. Amer. Math. Soc. 147 (2019), 2963-2973 Request permission
Abstract:
We prove an estimate for the capacity of the condenser $(\mathbb {D},K_{r})$, $r\in (0,1)$, where $\mathbb {D}$ is the open unit disc and $\{K_{r}\}$ is a compact exhaustion of the inverse image of a compact set under a Blaschke product $B$, involving weighted logarithmic integral means of the Frostman shifts of $B$. Also, we describe the asymptotic behavior of the capacity of condensers $(\mathbb {D},E_{r})$, where $E_{r}$ is a connected component of the inverse image of a closed disc with radius $r$ under universal covering maps as $r\to 0$.References
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Additional Information
- Dimitrios Betsakos
- Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
- MR Author ID: 618946
- Email: betsakos@math.auth.gr
- Georgios Kelgiannis
- Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
- Email: gkelgian@math.auth.gr
- Maria Kourou
- Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
- MR Author ID: 1257461
- Email: mkouroue@math.auth.gr
- Stamatis Pouliasis
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
- MR Author ID: 951898
- Email: stamatis.pouliasis@ttu.edu
- Received by editor(s): October 7, 2018
- Published electronically: April 3, 2019
- Additional Notes: This research has been co-financed by the Operational Program “Human Resources Development, Education and Lifelong Learning” and is co-financed by the European Union (European Social Fund) and Greek national funds.
- Communicated by: Stephan Ramon Garcia
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 2963-2973
- MSC (2010): Primary 30C85, 30J10, 30C80, 31A15
- DOI: https://doi.org/10.1090/proc/14585
- MathSciNet review: 3973898