Potential Theory in the Complex Plane

Ransford provides an introduction to the subject concentrating on the important case of two dimensions and emphasizing its links with complex analysis. This is reflected in the large number of applications which include Picard''s theorem the Phragmn-Lindelf principle the Rad-Stout theorem Lindelf''s theory of asymptotic values the Riemann mapping theorem (including continuity at the boundary) the Koebe one-quarter theorem Hilbert''s lemniscate theorem and the sharp quantitative form of Runge''s theorem. In addition there is a chapter on connections with functional analysis and dynamical systems which shows how the theory can be applied to other parts of mathematics and gives a flavor of some recent research in the area.