Volume 22, issue 1 (2018)

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

Volume 22
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
This article is available for purchase or by subscription. See below.
Complete minimal surfaces densely lying in arbitrary domains of $\mathbb{R}^n$

Antonio Alarcón and Ildefonso Castro-Infantes

Geometry & Topology 22 (2018) 571–590
Abstract

In this paper we prove that, given an open Riemann surface M and an integer n 3, the set of complete conformal minimal immersions M n with X(M)̄ = n forms a dense subset in the space of all conformal minimal immersions M n endowed with the compact-open topology. Moreover, we show that every domain in n contains complete minimal surfaces which are dense on it and have arbitrary orientable topology (possibly infinite); we also provide such surfaces whose complex structure is any given bordered Riemann surface.

Our method of proof can be adapted to give analogous results for nonorientable minimal surfaces in n(n 3), complex curves in n(n 2), holomorphic null curves in n(n 3), and holomorphic Legendrian curves in 2n+1(n ).

PDF Access Denied

Warning: We have not been able to recognize your IP address 54.196.13.210 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:

Keywords
complete minimal surface, Riemann surface, holomorphic curve
Mathematical Subject Classification 2010
Primary: 49Q05
Secondary: 32H02
References
Publication
Received: 15 November 2016
Accepted: 28 April 2017
Published: 31 October 2017
Proposed: Tobias H Colding
Seconded: Dmitri Burago, Leonid Polterovich
Authors
Antonio Alarcón
Departamento de Geometría y Topología
Universidad de Granada
Granada
Spain
http://www.ugr.es/~alarcon
Ildefonso Castro-Infantes
Departamento de Geometría y Topología
Universidad de Granada
Granada
Spain
http://www.ugr.es/~icastroinfantes