Algebraic approximation and the Mittag-Leffler theorem for minimal surfaces

Abstract

In this paper, we prove a uniform approximation theorem with interpolation for complete conformal minimal surfaces with finite total curvature in the Euclidean space ${\mathbb{R}}^n$ $(n\ge 3)$. As application, we obtain a Mittag-Leffler type theorem for complete conformal minimal immersions $M\to {\mathbb{R}}^n$ on any open Riemann surface $M$.

To appear in Analysis & PDE