This article is cited in 1 paper

On the $p$-harmonic radii of circular sectors

A. S. Afanaseva-Grigoreva^a, E. G. Prilepkina<sup>ba

a</sup> Far Eastern Federal University, Far Eastern Center for Research and Education in Mathematics, 10 Ajax Bay, Russky Island, Vladivostok 690922, Russia
^b Institute of Applied Mathematics, FEBRAS, 7 Radio Street, Vladivostok 690041, Russia

Abstract: It is proved that the property of logarithmic concavity of the conformal radius of a circular sector (considered as a function of the angle) extends to the domains of Euclidean space. In this case, the conformal radius is replaced by $p$-harmonic one, and the fundamental solution of the Laplace $p$-equation acts as logarithm. In the case of $p=2$, the presence of an asymptotic formula for the capacity of a degenerate condenser allows us to generalize this result to the case of a finite set of points. The method of the proof leads to the solution of one particular case of an open problem of A. Yu. Solynin.

Keywords: condenser capacities, conformal radius, harmonic radius, family of curves.

UDC: 517.54

MSC: 31B15

Received: 19.06.2021
Revised: 22.10.2021
Accepted: 27.10.2021

Language: English

DOI: 10.15393/j3.art.2021.10950

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