Geodesic
Two theorems on boundary properties of minimal surfaces in nonparametric form
Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 551-556 
V. M. Miklyukov. Two theorems on boundary properties of minimal surfaces in nonparametric form. Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 551-556. http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a12/
@article{MZM_1977_21_4_a12,
     author = {V. M. Miklyukov},
     title = {Two theorems on boundary properties of minimal surfaces in nonparametric form},
     journal = {Matemati\v{c}eskie zametki},
     pages = {551--556},
     year = {1977},
     volume = {21},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $D$ be a region with rectifiable Jordan boundary $\Gamma$, and let $z=f(x,y)$ be a minimal surface defined over $D$. This paper establishes that: 1) function $z=f(x,y)$ almost everywhere on $\Gamma$ has finite or infinite angular boundary values; 2) if region $D$ is the exterior of a circle then, almost everywhere on boundary $\Gamma$, function $z=f(x,y)$ can be continued by continuity.