Geodesic
On the conformal capacity of a spatial condenser with spherical plates
Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 1, pp. 76-83.

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Condencers with spherical plates are considered, the radii of which depend on the parameter r. It is shown that the conformal capacity of such condencers is a multiplicatively convex function of r. As a corollary, it has been established that some special functions related to capacity have a similar property. 
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E. G. Prilepkina. On the conformal capacity of a spatial condenser with spherical plates. Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 1, pp. 76-83. http://geodesic.mathdoc.fr/item/DVMG_2022_22_1_a6/

[1] V. Dubinin, Condenser Capacities and Symmetrization in Geometric Function Theory, Springer, Basel, 2014 | MR | Zbl

[2] J. Hesse, “A $p$-extremal length and $p$-capacity equalit”, Ark. mat., 13:1 (1975), 131–144 | DOI | MR | Zbl

[3] M. Vuorinen, “Conformal geometry and quasiregular mappings”, Lecture Notes in Mathematics, Springer-Verlag, 1988 | DOI | MR

[4] V. N. Dubinin, “Nekotorye svoistva vnutrennego privedennogo modulya”, Sib. matem. zhurn., 35:4 (1994), 774–-792 | MR | Zbl

[5] B. E. Levitskii, “Reduced $p$-modulus and the interior $p$-harmonic radius”, Dokl. Akad. Nauk SSSR, 316:4 (1991), 812–815 | MR | Zbl

[6] V. N. Dubinin, E. G. Prilepkina, “On extremal decomposition of $n$-space domains”, J. Math. Sci., 105:4 (2001), 2180–2189 | DOI | MR | Zbl

[7] G. D. Anderson, M.,K. Vamanamurthy and M. Vuorinen, “Special functions of quasiconformal theory”, Expositiones Mathematicae, 7 (1989), 97–138 | MR

[8] E. G. Prilepkina, A. S. Afanaseva-Grigoreva, “O konformnoi metrike krugovogo koltsa v n-mernom evklidovom prostranstve”, Dalnevost. matem. zhurn., 18:2 (2018), 233–-241 | MR | Zbl

[9] R. Laugesen, “Extremal problems involving logarithmic and Green capacity”, Duke Math. J., 70:2 (1993), 445–480 | DOI | MR | Zbl

[10] S. Pouliasis, “Concavity of condenser energy under boundary variations”, J. Geom. Anal., 31:8 (2021), 7726–7740 | DOI | MR | Zbl

[11] P. R. Garabedian, M. Schiffer, “Convexity of domain functionals”, J. Anal. Math., 2 (1953), 281–368 | DOI | MR | Zbl

[12] A. S. Afanaseva-Grigoreva, E. G. Prilepkina, “On the $p$-harmonic radii of circular sectors”, Issues Anal., 10(28):3 (2021), 3-–14 | DOI | MR

[13] V. N. Dubinin, “Green energy and extremal decompositions”, Probl. Anal. Issues Anal., 8(26):3 (2019), 38–44 | DOI | MR | Zbl

[14] V. N. Dubinin, E. G. Prilepkina, “Optimal Green energy points on the circles in $d$-space”, Journal of Mathematical Analysis and Applications, 499:2 (2021), 125055 | DOI | MR | Zbl