Abstract
We extend classical results by Lavrentiev and Kufarev concerning the product of the conformal radii of planar nonoverlapping domains. We also extend relatively recent results for the case of domains in the n-dimensional Euclidean space, n ≥ 3, with conformal radii replaced by harmonic ones. Namely, we get analogues of these results in n-dimensional Euclidean space in terms of p-harmonic radius. The proofs are based on the technique of moduli of curve families and dissymmetrization of such families.
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This work has been supported by the Russian Science Foundation under project 14-11-00022.
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Kalmykov, S., Prilepkina, E. Extremal decomposition problems for p-harmonic radius. Anal Math 43, 49–65 (2017). https://doi.org/10.1007/s10476-017-0103-y
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DOI: https://doi.org/10.1007/s10476-017-0103-y