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Some properties of the reduced modulus in space

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Abstract

We obtain upper bounds for the conformal modulus of a condenser with uniformly perfect plates and for the reduced modulus of a uniformly perfect set E at . For the reduced moduli of α-uniformly perfect sets we prove the continuity property with respect to the kernel convergence of the complements to these sets in the sense of Carathéodory.

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    O. A. Lazareva

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  1. O. A. Lazareva
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Correspondence to O. A. Lazareva.

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Original Russian Text Copyright © 2008 Lazareva O. A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 145–152, January–February, 2008.

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Lazareva, O.A. Some properties of the reduced modulus in space. Sib Math J 49, 117–122 (2008). https://doi.org/10.1007/s11202-008-0011-2

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  • DOI: https://doi.org/10.1007/s11202-008-0011-2

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