Generalized capacities, compound curves, and removable sets
Relations between the generalized capacity of a condenser in the sense of Aikawa-Ohtsuka and the module of the family of compound curves connecting the condenser plates through a given set are established. Conditions of the removability of a compact set for the generalized capacity of a condenser are obtained. Properties of the extremal length of vector measures are used. Bibliography: 9 titles.
KeywordsVector Measure Generalize Capacity Extremal Length Compound Curf
Unable to display preview. Download preview PDF.
- 1.K. Kuratowski, Topology, Vol. II [Russian translation], Mir, Moscow (1969).Google Scholar
- 2.P. A. Pugach and V. A. Shlyk, “Generalized capacities and polyhedral surfaces,” Zap. Nauchn. Semin. POMI, 383, 148–179 (2010).Google Scholar
- 3.P. A. Pugach and V. A. Shlyk, “Removable sets for the generalized module of a surface family,” Zap. Nauchn. Semin. POMI, 392, 163–190 (2011).Google Scholar
- 4.V. A. Shlyk, “Normal domains and removable singularities,” Izv. RAN, Ser. Mat., 57, 93–117 (1993).Google Scholar
- 9.M. Ohtsuka, Extremal Length and Precise Functions (GAKUTO Int. Ser. Math. Sci. Appl., 19), Gakkōtosho, Tokyo (2003).Google Scholar