A Minimal Lamination of the Unit Ball with Singularities along a Line Segment
Abstract
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.
Keywords
Cite
@article{arxiv.0902.3641,
title = {A Minimal Lamination of the Unit Ball with Singularities along a Line Segment},
author = {Siddique Khan},
journal= {arXiv preprint arXiv:0902.3641},
year = {2009}
}
Comments
updated page dimensions and documentclass to amsart; added a 3-dimensional schematic picture of the limit lamination; added a reference