Illinois Journal of Mathematics

The limit lamination metric for the Colding-Minicozzi minimal lamination

William H. Meeks, III

Full-text: Open access

Abstract

We prove that the singular set $S(\mathcal{L})$ of convergence in a Colding-Minicozzi limit minimal lamination $\lc$ is a $C^{1,1}$-curve which is orthogonal to leaves of the limit minimal lamination $\mathcal{L}$ in some neighborhood of $\mathcal{S}(\mathcal{L})$. We also obtain useful information on the related limit lamination metric.

Article information

Source
Illinois J. Math., Volume 49, Number 2 (2005), 645-658.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138037

Digital Object Identifier
doi:10.1215/ijm/1258138037

Mathematical Reviews number (MathSciNet)
MR2164355

Zentralblatt MATH identifier
1087.53058

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Meeks, William H. The limit lamination metric for the Colding-Minicozzi minimal lamination. Illinois J. Math. 49 (2005), no. 2, 645--658. doi:10.1215/ijm/1258138037. https://projecteuclid.org/euclid.ijm/1258138037


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