This article is cited in 2 papers

About polarization with respect to hypersphere

E. V. Kostyuchenko, E. G. Prilepkina

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: Polarization with respect to hypersphere is expressed with the help of conformal mappings through polarization of flat sets with respect to a straight line. It is formulated continuous (partial) simmetrization with respect to hypersphere in euclidean $n$-space. As an application of the new representation of hypersphere-polarization the non-increasing of the conformal capacity of condenser is proved.

Key words: condenser, conformal capacity, simmetrization, polarization.

UDC: 517.54

MSC: 31A15

Received: 30.03.2004

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