Two theorems on boundary properties of minimal surfaces in nonparametric form

Abstract

Let D be a region with rectifiable Jordan boundary Γ, 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 Γ has finite or infinite angular boundary values; 2) if region D is the exterior of a circle then, almost everywhere on boundary Γ, function z=f(x, y) can be continued by continuity.