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Keywords:

  • Omitted area problem;
  • logarithmic capacity;
  • univalent function;
  • symmetrization;
  • local variation;
  • MSC (2010) 30C70

Abstract

We consider the complex plane equation image as a space filled by two different media, separated by the real axis equation image. We define equation image to be the upper half-plane. For a planar body E in equation image, we discuss a problem of estimating characteristics of the “invisible” part, equation image, from characteristics of the whole body E and its “visible” part, equation image. In this paper, we find the maximal draft of E as a function of the logarithmic capacity of E and the area of E+.