English

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.

Keywords

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