Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 53, Number 3 (2009), 833-855.
A minimal lamination of the unit ball with singularities along a line segment
We construct a sequence of compact embedded minimal disks in the unit ball in Euclidean 3-space whose boundaries are in the boundary of the ball and where the curvatures blow up at every point of a line segment of the vertical axis, extending from the origin. We further study the transversal structure of the minimal limit lamination and find removable singularities along the line segment and a non-removable singularity at the origin. This extends a result of Colding and Minicozzi where they constructed a sequence with curvatures blowing up only at the center of the ball, Dean’s construction of a sequence with curvatures blowing up at a prescribed discrete set of points, and the classical case of the sequence of re-scaled helicoids with curvatures blowing up along the entire vertical axis.
Illinois J. Math., Volume 53, Number 3 (2009), 833-855.
First available in Project Euclid: 4 October 2010
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Khan, Siddique. A minimal lamination of the unit ball with singularities along a line segment. Illinois J. Math. 53 (2009), no. 3, 833--855. doi:10.1215/ijm/1286212918. https://projecteuclid.org/euclid.ijm/1286212918