Far Eastern Mathematical Journal

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


Prilepkina E.G.

2017, issue 2, Ñ. 246-256


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.

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

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