Iceberg-type Problems: Estimating Hidden Parts of a Continuum from the Visible Parts

Roger Barnard, Kent Pearce, Alexander Solynin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the complex plane C as a space filled by two different media, separated by the real axis R. Let H+={z: Im z > 0} be the upper half-plane. For a planar body E, the general iceberg-type problem is to estimate 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+.
Original languageEnglish
Pages (from-to)2042-2058
JournalMathematische Nachricthen
DOIs
StatePublished - Dec 1 2012

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