Convex expansion of condenser plates
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 3-15.

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In this paper we consider the Möbius invariant operation of convex expansion of condenser plates in the space Rn. In the case n=2 we prove that this operation cannot increase the capacity of a condenser with connected plates more than 3 times.
Mots-clés : condenser, conformal capacity, convexity, Möbius transformation, Möbius invariance, modulus of a curve family, condenser loading.
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V. V. Aseev. Convex expansion of condenser plates. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 3-15. https://geodesic-test.mathdoc.fr/item/IVM_2010_8_a0/

[1] Reshetnyak Yu. G., “Ob odnom obobschenii vypuklykh poverkhnostei”, Matem. sb., 40(82):3 (1956), 381–398 | MR | Zbl

[2] Golubyatnikov V. P., Rovenski V., Some extensions of the class of convex bodies, arXiv: 0808.1788v1

[3] Dubinin V. N., “Simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo”, UMN, 49:1 (1994), 3–76 | MR | Zbl

[4] Solynin A. Yu., “Moduli i ekstremalno-metricheskie problemy”, Algebra i analiz, 11:1 (1999), 3–86 | MR | Zbl

[5] Nasyrov S. R., “Variatsii emkostei Robena i ikh prilozheniya”, Sib. matem. zhurn., 49:5 (2008), 1128–1146 | MR

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

[7] Aseev V. V., Sychev A. V., Zapolnenie kondensatorov i skhodimost k yadru, Preprint 146, In-t matem. SO RAN, Novosibirsk, 2004

[8] Aseev V. V., Sychev A. V., “Zapolnenie kondensatorov i skhodimost k yadru”, Vestn. NGU, 5:3 (2005), 3–19

[9] Aseev V. V., “Faktorizatsiya prostranstva kondensatorov i skhodimost k yadru”, Dokl. RAN, 419:5 (2008), 583–586 | MR | Zbl

[10] Moreno J. P., “An invitation to plane topology”, Austral. Math. Soc. Gaz., 29:3 (2002), 149–154 | MR | Zbl

[11] Kuratovskii K., Topologiya, v. 2, Mir, M., 1969 | MR

[12] Fuglede B., “Extremal length and functional completion”, Acta Math., 98 (1957), 171–219 | DOI | MR | Zbl

[13] Väisälä J., “Lectures on $n$-dimentional quasiconformal mappings”, Lect. Notes Math., 229, 1971, 1–144 | MR

[14] Vuorinen M., “Conformal geometry and quasiregular mappings”, Lect. Notes Math., 1319, 1988, 1–210 | MR