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 n (n 3). As application, we obtain a Mittag-Leffler-type theorem for complete conformal minimal immersions M 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