Translator Disclaimer
15 June 2006 The minimal lamination closure theorem
William H. Meeks III, Harold Rosenberg
Author Affiliations +
Duke Math. J. 133(3): 467-497 (15 June 2006). DOI: 10.1215/S0012-7094-06-13332-X

Abstract

We prove that the closure of a complete embedded minimal surface M in a Riemannian three-manifold N has the structure of a minimal lamination when M has positive injectivity radius. When N is R3, we prove that such a surface M is properly embedded. Since a complete embedded minimal surface of finite topology in R3 has positive injectivity radius, the previous theorem implies a recent theorem of Colding and Minicozzi in [5, Corollary 0.7]; a complete embedded minimal surface of finite topology in R3 is proper. More generally, we prove that if M is a complete embedded minimal surface of finite topology and N has nonpositive sectional curvature (or is the Riemannian product of a Riemannian surface with R), then the closure of M has the structure of a minimal lamination

Citation

Download Citation

William H. Meeks III. Harold Rosenberg. "The minimal lamination closure theorem." Duke Math. J. 133 (3) 467 - 497, 15 June 2006. https://doi.org/10.1215/S0012-7094-06-13332-X

Information

Published: 15 June 2006
First available in Project Euclid: 13 June 2006

zbMATH: 1098.53007
MathSciNet: MR2228460
Digital Object Identifier: 10.1215/S0012-7094-06-13332-X

Subjects:
Primary: 53A10
Secondary: 49Q05 , 53C42

Rights: Copyright © 2006 Duke University Press

JOURNAL ARTICLE
31 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.133 • No. 3 • 15 June 2006
Back to Top