TY - JOUR

T1 - Iceberg-type Problems: Estimating Hidden Parts of a Continuum from the Visible Parts

AU - Barnard, Roger

AU - Pearce, Kent

AU - Solynin, Alexander

PY - 2012/12/1

Y1 - 2012/12/1

N2 - 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+.

AB - 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+.

U2 - 10.1002/mana.200710056/pdf

DO - 10.1002/mana.200710056/pdf

M3 - Article

SP - 2042

EP - 2058

JO - Mathematische Nachricthen

JF - Mathematische Nachricthen

ER -