Iceberg-type problems: Estimating Hidden parts of a continuum from the visible parts

Authors

  • Roger W. Barnard,

    1. Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409, USA
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  • Kent Pearce,

    Corresponding author
    1. Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409, USA
    • Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409, USA. Phone: +1 806 742 2566, Fax: +1 8706 742 1112
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  • Alexander Yu. Solynin

    Corresponding author
    1. Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409, USA
    • Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409, USA. Phone: +1 806 742 2566, Fax: +1 8706 742 1112
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Abstract

We consider the complex plane equation image as a space filled by two different media, separated by the real axis equation image. We define equation image to be the upper half-plane. For a planar body E in equation image, we discuss a problem of estimating characteristics of the “invisible” part, equation image, from characteristics of the whole body E and its “visible” part, equation image. In this paper, we find the maximal draft of E as a function of the logarithmic capacity of E and the area of E+.

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