This article is cited in 3 papers

The generalized reduced modulus in spatial problems of the capacitorial tomography

V. V. Aseev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The external problem of the spatial capacitorial tomography is considered. The notion of capacitorial defect of an object (a compact set) along Möbius directions in the space has been introduced. The criteria for the capacitorial invisibility of an object along the Möbius direction determined by a pair of points in the accessible region of the space has been obtained. The problem of upper estimates for the capacitorial defect along Möbius directions in the space, as well as it's connection with the notion of generalized reduced modulus by V.N. Dubinin, is there also considered in this paper.

Key words: condenser, conformal capacity, conformal modulus, modulus of a set of curves, capacitorial defect, capacitorial tomography, capacitorial invisibility, NED-set, eliminability along direction, Apollonian condenser, generalized reduced modulus.

UDC: 517.54, 517.956

MSC: Primary 31A15; Secondary 30C85

Received: 26.11.2007

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