Embedded minimal disks with prescribed curvature blowup
Differential Geometry
2007-05-23 v1
Abstract
We construct a sequence of compact embedded minimal disks in a ball in Euclidean 3-space, whose boundaries lie in the boundary of the ball, such that the curvature blows up only at a prescribed discrete (and hence, finite) set of points on the x_3-axis. This extends a result of Colding and Minicozzi, who constructed a sequence for which the curvature blows up only at the center of the ball, and is a partial affirmative answer to the larger question of the existence of a sequence for which the curvature blows up precisely on a prescribed closed set on the x_3-axis.
Cite
@article{arxiv.math/0408079,
title = {Embedded minimal disks with prescribed curvature blowup},
author = {Brian Dean},
journal= {arXiv preprint arXiv:math/0408079},
year = {2007}
}
Comments
10 pages, 0 figures, preprint