Condenser capacity, exponential Blaschke products and universal covering maps

Mashreghi, Javad; Pouliasis, Stamatis

doi:10.1090/S0002-9939-2015-12516-6

Condenser capacity, exponential Blaschke products and universal covering maps
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by Javad Mashreghi and Stamatis Pouliasis PDF

Proc. Amer. Math. Soc. 143 (2015), 3547-3559 Request permission

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 $K_{n}=B^{-1}(C)\cap \{z\in \mathbb {D}:|z|\leq 1-2^{-n}\}$. 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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