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 language | English |
|---|---|
| Pages (from-to) | 2042-2058 |
| Number of pages | 17 |
| Journal | Mathematische Nachrichten |
| Volume | 285 |
| Issue number | 17-18 |
| DOIs | |
| State | Published - Dec 2012 |
Keywords
- Local variation
- Logarithmic capacity
- Omitted area problem
- Symmetrization
- Univalent function
Fingerprint Dive into the research topics of 'Iceberg-type problems: Estimating Hidden parts of a continuum from the visible parts'. Together they form a unique fingerprint.
Cite this
Barnard, R. W., Pearce, K., & Solynin, A. Y. (2012). Iceberg-type problems: Estimating Hidden parts of a continuum from the visible parts. Mathematische Nachrichten, 285(17-18), 2042-2058. https://doi.org/10.1002/mana.200710056