Vol. 12, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 3, 567–890
Issue 2, 273–566
Issue 1, 1–272

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Interpolation by conformal minimal surfaces and directed holomorphic curves

Antonio Alarcón and Ildefonso Castro-Infantes

Vol. 12 (2019), No. 2, 561–604
DOI: 10.2140/apde.2019.12.561

Let M be an open Riemann surface and n 3 be an integer. We prove that on any closed discrete subset of M one can prescribe the values of a conformal minimal immersion M n . Our result also ensures jet-interpolation of given finite order, and hence, in particular, one may in addition prescribe the values of the generalized Gauss map. Furthermore, the interpolating immersions can be chosen to be complete, proper into n if the prescription of values is proper, and injective if n 5 and the prescription of values is injective. We may also prescribe the flux map of the examples.

We also show analogous results for a large family of directed holomorphic immersions M n , including null curves.

Dedicated to Franc Forstnerič on the occasion of his sixtieth birthday

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

minimal surface, directed holomorphic curve, Weierstrass theorem, Riemann surface, Oka manifold
Mathematical Subject Classification 2010
Primary: 53A10, 32E30, 32H02, 53A05
Received: 1 March 2018
Accepted: 1 May 2018
Published: 14 August 2018
Antonio Alarcón
Departamento de Geometría y Topología
Instituto de Matemáticas (IEMath-GR)
Universidad de Granada
Campus de Fuentenueva
Ildefonso Castro-Infantes
Departamento de Geometría y Topología
Instituto de Matemáticas (IEMath-GR)
Universidad de Granada
Campus de Fuentenueva