Geodesic
Sufficiency of Polyhedral Surfaces in the Modulus Method and Removable Sets
Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 216-230.

Voir la notice de l'article provenant de la source Math-Net.Ru

The sufficiency of a family of polyhedral surfaces for calculating the modulus of a family of surfaces separating the plates of a condenser in an open set is proved. Geometric properties of removable sets for this modulus are also determined.
Keywords: modulus of a family of surfaces, surface separating plates of a condenser, removable set for a modulus of a family of surfaces, polyhedral surface, Borel function, Hölder inequality.
Mots-clés : condenser, Lebesgue and Hausdorff measure 
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Yu. V. Dymchenko; V. A. Shlyk. Sufficiency of Polyhedral Surfaces in the Modulus Method and Removable Sets. Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 216-230. http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a4/

[1] W. P. Ziemer, “Extremal length and conformal capacity”, Trans. Amer. Math. Soc., 126:3 (1967), 460–473 | DOI | MR | Zbl

[2] V. A. Shlyk, “Emkost kondensatora i modul semeistva razdelyayuschikh poverkhnostei”, Analiticheskaya teoriya chisel i teoriya funktsii. 10, Zap. nauchn. sem. POMI, 185, Izd-vo «Nauka», Leningrad. otd., L., 1990, 168–182 | MR | Zbl

[3] Yu. V. Dymchenko, V. A. Shlyk, “Sootnoshenie mezhdu vesovoi emkostyu kondensatora i vesovym modulem semeistva razdelyayuschikh poverkhnostei”, Dalnevost. matem. sb., 1996, no. 2, 72–80 | MR | Zbl

[4] L. I. Hedberg, “Removable singularities and condenser capacities”, Ark. Mat., 12:1-2 (1974), 181–201 | DOI | MR | Zbl

[5] I. N. Demshin, V. A. Shlyk, “Kriterii ustranimykh mnozhestv dlya vesovykh prostranstv garmonicheskikh funktsii”, Analiticheskaya teoriya chisel i teoriya funktsii. 18, Zap. nauchn. sem. POMI, 286, POMI, SPb., 2002, 62–73 | MR | Zbl

[6] V. V. Aseev, “NED-mnozhestva, lezhaschie v giperploskosti”, Sib. matem. zhurn., 50:5 (2009), 967–986 | MR | Zbl

[7] B. Muckenhoupt, “Weighted norm inequalities for the Hardy maximal functions”, Trans. Amer. Math. Soc., 165 (1972), 207–226 | DOI | MR | Zbl

[8] M. Ohtsuka, Extremal Length and Precise Functions, GAKUTO Internat. Ser. Math. Sci. Appl., 19, Gakkōtosho, Tokyo, 2003 | MR | Zbl

[9] B. Fuglede, “Extremal length and functional completion”, Acta Math., 98:3 (1957), 171–219 | DOI | MR | Zbl

[10] H. Federer, W. H. Fleming, “Normal and integral currents”, Ann. of Math. (2), 72:3 (1960), 458–520 | DOI | MR | Zbl

[11] V. A. Shlyk, “Vesovye emkosti, moduli kondensatorov i isklyuchitelnye mnozhestva po Fyuglede”, Dokl. RAN, 332:4 (1993), 428–431 | MR | Zbl

[12] Yu. V. Dymchenko, V. A. Shlyk, “Geometricheskie kriterii ustranimykh mnozhestv”, Analiticheskaya teoriya chisel i teoriya funktsii. 23, Zap. nauchn. sem. POMI, 357, POMI, SPb., 2008, 75–89 | MR | Zbl