Duke Mathematical Journal
- Duke Math. J.
- Volume 133, Number 3 (2006), 467-497.
The minimal lamination closure theorem
We prove that the closure of a complete embedded minimal surface in a Riemannian three-manifold has the structure of a minimal lamination when has positive injectivity radius. When is , we prove that such a surface is properly embedded. Since a complete embedded minimal surface of finite topology in 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 is proper. More generally, we prove that if is a complete embedded minimal surface of finite topology and has nonpositive sectional curvature (or is the Riemannian product of a Riemannian surface with ), then the closure of has the structure of a minimal lamination
Duke Math. J., Volume 133, Number 3 (2006), 467-497.
First available in Project Euclid: 13 June 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 49Q05: Minimal surfaces [See also 53A10, 58E12] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Meeks, William H.; Rosenberg, Harold. The minimal lamination closure theorem. Duke Math. J. 133 (2006), no. 3, 467--497. doi:10.1215/S0012-7094-06-13332-X. https://projecteuclid.org/euclid.dmj/1150201199