Far Eastern Mathematical Journal

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About polarization with respect to hypersphere


E. V. Kostyuchenko, E. G. Prilepkina

2004, issue 1, Ñ. 22–29


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.

Keywords:
condenser, conformal capacity, simmetrization, polarization

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References

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