TY - JOUR
T1 - Iceberg-type problems
T2 - Estimating Hidden parts of a continuum from the visible parts
AU - Barnard, Roger W.
AU - Pearce, Kent
AU - Solynin, Alexander Yu
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/12
Y1 - 2012/12
N2 - 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+.
AB - 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+.
KW - Local variation
KW - Logarithmic capacity
KW - Omitted area problem
KW - Symmetrization
KW - Univalent function
UR - http://www.scopus.com/inward/record.url?scp=84870432216&partnerID=8YFLogxK
U2 - 10.1002/mana.200710056
DO - 10.1002/mana.200710056
M3 - Article
AN - SCOPUS:84870432216
VL - 285
SP - 2042
EP - 2058
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 17-18
ER -