On Functions with a Conjugate
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Baird, Paul
Eastwood, Michael
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Association des Annales de l'Institut Fourier
Abstract
Harmonic functions of two variables are exactly those that admit
a conjugate, namely a function whose gradient has the same length and is
everywhere orthogonal to the gradient of the original function. We show that there
are also partial differential equations controlling the functions of three variables
that admit a conjugate.
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Annales de l'institut Fourier
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