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Siberian Mathematical Journal

, 50:760 | Cite as

Ned sets on a hyperplane

  • V. V. AseevEmail author
Article

Abstract

Under study are the sets in ℝ n (NED sets) each of which does not affect the conformal capacity of any condenser with connected plates disjoint from this set. These sets are removable singularities of quasiconformal mappings, which explains our interest in them. For compact sets on a hyperplane we obtain a geometric criterion of the NED property; we point out a simple sufficient condition for an NED set in terms of the connected attainability of its points from its complement in the hyperplane. For compact sets on a hypersphere we obtain a criterion for an NED set in terms of the reduced module at a pair of points in its complement. We establish that a compact set on a hypersphere S, removable for the capacity in at least one spherical ring concentric with S and containing S, is an NED set.

Keywords

module of a family of curves NED set quasiconformal mapping removable singularity capacity of a condenser reduced generalized module capacity defect attainable boundary point 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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