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Two problems in the theory of unique determination of domains

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We obtain estimates for the absolute and relative conformal moduli of a boundary condenser with two parallel segments. We prove that the convexity of a planar domain U with smooth boundary does not imply, in general, the unique determination of U in the class of all planar domains with smooth boundaries by the condition of the local isometry of the boundaries in their relative metrics. Bibliography: 7 titles. Illustrations: 1 figure.

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  1. Sobolev Institute of Mathematics SB RAS, 4, pr. Akad. Koptyuga, Novosibirsk, 630090, Russia

    D. A. Slutskii

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  1. D. A. Slutskii
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Correspondence to D. A. Slutskii.

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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 11, No. 2, 2011, pp. 93–104

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Slutskii, D.A. Two problems in the theory of unique determination of domains. J Math Sci 188, 463–473 (2013). https://doi.org/10.1007/s10958-012-1143-2

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  • DOI: https://doi.org/10.1007/s10958-012-1143-2

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