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

Roger W. Barnard, Kent Pearce, Alexander Yu Solynin

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We consider the complex plane C{double-struck} as a space filled by two different media, separated by the real axis R{double-struck}. We define H{double-struck}+={z: z>0} to be the upper half-plane. For a planar body E in C{double-struck}, we discuss a problem of estimating characteristics of the "invisible" part, E-=E\H{double-struck}, 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
Number of pages17
JournalMathematische Nachrichten
Volume285
Issue number17-18
DOIs
StatePublished - Dec 2012

Keywords

  • Local variation
  • Logarithmic capacity
  • Omitted area problem
  • Symmetrization
  • Univalent function

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