Two theorems on boundary properties of minimal surfaces in nonparametric form

V. M. Miklyukov

Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 551-556

Résumé

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.