Potential theory is the broad area of mathematical analysis
encompassing such topics as harmonic and subharmonic functions, the
Dirichlet problem, harmonic measure, Green's functions, potentials
and capacity. This is an introduction to the subject suitable for
beginning graduate students, concentrating on the important case of
two dimensions. This permits a simpler treatment than other books,
yet is still sufficient for a wide range of applications to complex
analysis; these include Picard's theorem, the Phragmen-Lindeloef
principle, the Koebe one-quarter mapping theorem and a 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 flavour of some recent research.
Exercises are provided throughout, enabling the book to be used
with advanced courses on complex analysis or potential theory.
General
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