#### Vol. 15, No. 3, 2022

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Algebraic approximation and the Mittag-Leffler theorem for minimal surfaces

### Antonio Alarcón and Francisco J. López

Vol. 15 (2022), No. 3, 859–890
##### Abstract

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

##### Keywords
minimal surface, Riemann surface, meromorphic function
##### Mathematical Subject Classification
Primary: 30D30, 32E30, 53A10, 53C42