Geometric criteria for removable sets. (English. Russian original) Zbl 1182.31015
J. Math. Sci., New York 157, No. 4, 584-591 (2009); translation from Zap. Nauchn. Semin. POMI 357, 75-89 (2008).
Summary: The paper presents same exact geometric characteristics of removable sets for two classes of weighted capacities.
MSC:
| 31C15 | Potentials and capacities on other spaces |
References:
| [1] | P. Natanson, The Theory of Functions of a Real Variable [in Russian], St. Petersburg (1999). |
| [2] | V. A. Shlyk, ”Condenser’s capacity and the module of a family of separating surfaces,” Zap. Nauchn. Semin. LOMI, 185, 168–182 (1990). · Zbl 0734.31008 |
| [3] | V. A. Shlyk, ”Metric characteristics of N p -compacts and of removable singularities of the space L p 1, p(1, ,” Zap. Nauchn. Semin. LOMI, 196, 162–171 (1991). · Zbl 0780.30021 |
| [4] | M. Ohtsuka, Extremal Length and Precise Functions, Gakkōtosho, Tokyo (2003). · Zbl 1075.31001 |
| [5] | W. P. Ziemer, ”Extremal length and conformal capacity,” Trans. Amer. Math. Soc., 126, No. 3, 460–473 (1967), · Zbl 0177.34002 · doi:10.1090/S0002-9947-1967-0210891-0 |
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