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 R n (n ≥ 3). As application, we obtain a Mittag-Leffler type theorem for complete conformal minimal immersions M → R n on any open Riemann surface M .

Minimal surfaces in Euclidean spaces by way of complex analysis

“…Parts (i), (ii) and (iv) are due to Alarcón, López, and myself [6,13,12] (the special case of (i) for = 3 was obtained beforehand in [19]), while (iii) was proved by Alarcón and Castro-Infantes [2,3]. Related results for conformal minimal surfaces of finite total curvature were given by Alarcón and López [18].…”