A Minimal Lamination of the Unit Ball with Singularities along a Line Segment
| dc.creator | Khan, Siddique | |
| dc.date | 2009-02-20 | |
| dc.date | 2009-04-01 | |
| dc.date.accessioned | 2026-07-07T12:58:25Z | |
| dc.date.available | 2026-07-07T12:58:25Z | |
| dc.description | 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. | |
| dc.description | updated page dimensions and documentclass to amsart; added a 3-dimensional schematic picture of the limit lamination; added a reference | |
| dc.identifier | https://arxiv.org/abs/0902.3641 | |
| dc.identifier | http://arxiv.org/abs/0902.3641 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225234 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53A10; 49Q05 | |
| dc.title | A Minimal Lamination of the Unit Ball with Singularities along a Line Segment | |
| dc.type | text |