On Functions with a Conjugate
Annales de l'Institut Fourier, Volume 65 (2015) no. 1, p. 277-314

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.

Les fonctions harmoniques en deux variables sont exactement celles qui admettent une fonction conjuguée, à savoir une fonction dont le gradient a la même longueur et est partout orthogonal au gradient de la fonction d’origine. Nous montrons qu’il existe des équations aux dérivées partielles qui contrôlent également les fonctions de trois variables qui admettent une fonction conjuguée.

DOI : https://doi.org/10.5802/aif.2931
Classification:  53A30
Keywords: conjugate function, conformal invariant, partial differential inequality, partial differential equation, 3-harmonic function, conformal Killing field
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     author = {Baird, Paul and Eastwood, Michael},
     title = {On Functions with a Conjugate},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {65},
     number = {1},
     year = {2015},
     pages = {277-314},
     doi = {10.5802/aif.2931},
     zbl = {06496540},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2015__65_1_277_0}
}
Baird, Paul; Eastwood, Michael. On Functions with a Conjugate. Annales de l'Institut Fourier, Volume 65 (2015) no. 1, pp. 277-314. doi : 10.5802/aif.2931. http://www.numdam.org/item/AIF_2015__65_1_277_0/

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