Geodesic
On the $p$-harmonic radii of circular sectors
Problemy analiza, Tome 10 (2021) no. 3, pp. 3-14

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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. 
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A. S. Afanaseva-Grigoreva; E. G. Prilepkina. On the $p$-harmonic radii of circular sectors. Problemy analiza, Tome 10 (2021) no. 3, pp. 3-14. http://geodesic.mathdoc.fr/item/PA_2021_10_3_a0/