This is a short introduction to the theory of the logarithmic potential. in the complex plane. The central ideas are the concepts of energy and equilibrium. We prove some classical results characterizing the equilibrium distribution and discuss the extension of these notions to more general settings when an external field or constraints on the distribution are present. The tools provided by potential theory have a profound impact on different branches of analysis. We illustrate these applications with two examples from approximation theory and complex dynamics.
CITATION STYLE
Finkelshtein, A. M. (2006). Equilibrium problems of potential theory in the complex plane. Lecture Notes in Mathematics, 1883, 79–117. https://doi.org/10.1007/978-3-540-36716-1_2
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