This article is cited in 2 scientific papers (total in 2 papers)
On the reduced modulus of the complex sphere
V. N. Dubininab
a Institute of Applied Mathematics, Vladivostok, Russia
b Far-Eastern Federal University, Vladivostok, Russia
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.
reduced modulus, condenser, capacity of a condenser, logarithmic capacity.
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Siberian Mathematical Journal, 2014, 55:5, 882–892
V. N. Dubinin, “On the reduced modulus of the complex sphere”, Sibirsk. Mat. Zh., 55:5 (2014), 1078–1090; Siberian Math. J., 55:5 (2014), 882–892
Citation in format AMSBIB
\paper On the reduced modulus of the complex sphere
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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V. N. Dubinin, “Inequalities for harmonic measures with respect to non-overlapping domains”, Izv. Math., 79:5 (2015), 902–918
V. N. Dubinin, “Some unsolved problems about condenser capacities on the plane”, Complex Analysis and Dynamical Systems: New Trends and Open Problems, Trends in Mathematics, eds. M. Agranovsky, A. Golberg, F. Jacobzon, D. Shoikhet, L. Zalcman, Birkhauser Verlag Ag, 2018, 81–92
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