Abstract
Abstract
This chapter discusses flows and harmonic functions. Both the real and the imaginary parts of an analytic function are automatically harmonic. It is therefore natural to wonder if, conversely, every harmonic function is the real (or imaginary) part of some analytic function. As the chapter demonstrates, this is indeed the case. That is, given a harmonic function u, one can always find another harmonic function v, the harmonic dual of u, such that f = u + iv is analytic. The harmonic dual of a single-valued function may itself be a multifunction. The chapter then looks at the conformal invariance of harmonicity and of the Laplacian; complex curvature; flow around an obstacle; the physics of Riemann’s Mapping Theorem; and Dirichlet’s problem.
Publisher
Oxford University PressOxford
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