Roger W. Barnard: Iceberg-type Problems: Estimating Hidden Parts of a Continuum from the Visible Parts

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 the 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 talk we determine the maximal draft of E as a function of the logarithmic capacity of E and the area of E+. We then discuss the problem for the more naturally occurring domains that are convex and those with more general type boundaries. Joint work with K.Pearce, A .Yu. Solynin and M. Lochman