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Paul Baird; Michael Eastwood
On Functions with a Conjugate
(Sur les fonctions qui admettent une fonction conjuguée)
Annales de l'institut Fourier, 65 no. 1 (2015), p. 277-314, doi: 10.5802/aif.2931
Article PDF | Reviews Zbl 06496540
Class. Math.: 53A30
Keywords: conjugate function, conformal invariant, partial differential inequality, partial differential equation, 3-harmonic function, conformal Killing field

Résumé - 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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