# Algebraic approximation and the Mittag-Leffler theorem for minimal surfaces

## TL;DR

This paper develops algebraic approximation techniques for complete conformal minimal surfaces with finite total curvature in Euclidean spaces, leading to a Mittag-Leffler type theorem for minimal immersions on open Riemann surfaces.

## Contribution

It introduces a uniform approximation theorem with interpolation for minimal surfaces, extending classical results to higher dimensions and more general surfaces.

## Key findings

- Proves a uniform approximation theorem with interpolation for minimal surfaces.
- Establishes a Mittag-Leffler type theorem for minimal immersions.
- Applies results to open Riemann surfaces in Euclidean spaces.

## 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 $M$.