Iceberg-type Problems: Estimating Hidden Parts of a Continuum from the Visible Parts
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چکیده
We consider the complex plane C as a space filled by two different media, separated by the real axis R. We define H+ = {z : = z > 0} to be the upper half-plane. For a planar body E in C, we discuss a problem of estimating characteristics of the “invisible” part, E− = E \H+, from characteristics of the whole body E and its “visible” part, E+ = E ∩ H+. 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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تاریخ انتشار 2008