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On the reduced modulus of the complex sphere

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Abstract

The notion of reduced modulus of the Riemann sphere with respect to a collection of finite points is extended to the case when the condenser plates are arbitrary continua contracting to these points. It is demonstrated that the reduced modulus is independent of the form of degenerate condenser plates. The reduced modulus was considered earlier in the case when the condenser plates are elements of families of almost disks with fixed centers.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Far-Eastern Federal University, Vladivostok, Russia

    V. N. Dubinin

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  1. V. N. Dubinin
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Correspondence to V. N. Dubinin.

Additional information

Original Russian Text Copyright © 2014 Dubinin V.N.

The author was partially supported by the Russian Scientific Foundation (Grant 14-11-00022).

To Yuriĭ Grigor’evich Reshetnyak on his 85th birthday.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 5, pp. 1078–1090, September–October, 2014.

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Dubinin, V.N. On the reduced modulus of the complex sphere. Sib Math J 55, 882–892 (2014). https://doi.org/10.1134/S0037446614050073

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  • DOI: https://doi.org/10.1134/S0037446614050073

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