Complete non-orientable minimal surfaces of finite total curvature: Approximation and interpolation

Abstract

In this paper, we prove a uniform approximation theorem with interpolation for complete non-orientable minimal surfaces of finite total curvature in the Euclidean space ${\mathbb{R}}^n$ $(n\ge 3)$. In particular, we establish the existence of such surfaces with the complex structure of any open conformal non-orientable surface of finite topology and parabolic type.