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Dal'nevost. Mat. Zh., 2017, Volume 17, Number 2, Pages 246–256 (Mi dvmg357)  

On the $n$-harmonic radius of domains in the n-dimensional Euclidean space

E. G. Prilepkinaab

a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok

Abstract: We extend a classical result by Lavrent’ev concerning the product of the conformal radii of planar non-overlapping domains to the case of domains in the n-dimensional Euclidean space. The conformal radius is then replaced by the n-harmonic Levitskii radius and the non-overlapping condition is replaced by a weaker geometric condition. The proofs are based on the technique of modulii of curve families. Conformal invariance of the module plays an important role in the proofs. Using the same method, we extend a classical result of Kufarev concerning the product of the conformal radii of planar non-overlapping domains in the unit disk. In addition, an inequality for n-harmonic radius of a star-shaped domain has been proved.

Key words: conformal radius, harmonic radius, modulii of curve families, extremal decompositions, star-shaped domain

Funding Agency Grant Number
Russian Science Foundation 14-11-00022


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UDC: 517.54
MSC: 31B99
Received: 31.08.2017

Citation: E. G. Prilepkina, “On the $n$-harmonic radius of domains in the n-dimensional Euclidean space”, Dal'nevost. Mat. Zh., 17:2 (2017), 246–256

Citation in format AMSBIB
\Bibitem{Pri17}
\by E.~G.~Prilepkina
\paper On the $n$-harmonic radius of domains in the n-dimensional Euclidean space
\jour Dal'nevost. Mat. Zh.
\yr 2017
\vol 17
\issue 2
\pages 246--256
\mathnet{http://mi.mathnet.ru/dvmg357}
\elib{http://elibrary.ru/item.asp?id=32239886}


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