A Minimal Lamination of the Unit Ball with Singularities along a Line Segment

Details A Minimal Lamination of the Unit Ball with Singularities along a Line Segment A Minimal Lamination of the Unit Ball with Singularities along a Line Segment

2009-02-20

arxiv.org/abs/0902.3641v2

Mathematics

Differential Geometry

updated page dimensions and documentclass to amsart; added a 3-dimensional schematic picture of the limit lamination; added a

Scientific paper

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.

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