Asymptotic values of minimal graphs in a disc
Annales de l'Institut Fourier, Volume 60 (2010) no. 7, p. 2357-2372

We consider solutions of the prescribed mean curvature equation in the open unit disc of euclidean n-dimensional space. We prove that such a solution has radial limits almost everywhere; which may be infinite. We give an example of a solution to the minimal surface equation that has finite radial limits on a set of measure zero, in dimension two. This answers a question of Nitsche.

Nous considérons les solutions de l´équation de la courbure moyenne prescrite sur le disque unité ouvert de l’espace euclidien. Nous prouvons qu’une telle solution a une limite radiale presque partout qui, éventuellement, peut-être infinie. Nous donnons l´exemple d´une solution de l´équation des surfaces minimales en dimension deux, qui admet des limites radiales finies sur un ensemble de mesure nulle. Ce travail répond à une question de Nitsche.

Classification:  53A10,  53C43
Keywords: Minimal graphs, radial limits, Fatou theorem
     author = {Collin, Pascal and Rosenberg, Harold},
     title = {Asymptotic values of minimal graphs in~a~disc},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {7},
     year = {2010},
     pages = {2357-2372},
     doi = {10.5802/aif.2610},
     mrnumber = {2849267},
     zbl = {1239.53004},
     language = {en},
     url = {}
Collin, Pascal; Rosenberg, Harold. Asymptotic values of minimal graphs in a disc. Annales de l'Institut Fourier, Volume 60 (2010) no. 7, pp. 2357-2372. doi : 10.5802/aif.2610.

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