Algebraic approximation and the Mittag-Leffler theorem for minimal surfaces

Alarcón, Antonio; López, Francisco J.

doi:10.2140/apde.2022.15.859

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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

DOI: 10.2140/apde.2022.15.859

Abstract

We prove a uniform approximation theorem with interpolation for complete conformal minimal surfaces with finite total curvature in the Euclidean space $ℝ^{n}$ ( $n \geq 3$ ). 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

Milestones

Received: 6 May 2020

Accepted: 27 October 2020

Published: 10 June 2022

Authors

Antonio Alarcón
Departamento de Geometría y Topología e Instituto de Matemáticas (IMAG) Universidad de Granada Granada Spain

Francisco J. López
Departamento de Geometría y Topología e Instituto de Matemáticas (IMAG) Universidad de Granada Granada Spain

Vol. 15, No. 3, 2022