Embedded minimal disks with prescribed curvature blowup

Details Embedded minimal disks with prescribed curvature blowup Embedded minimal disks with prescribed curvature blowup

2004-08-05

arxiv.org/abs/math/0408079v1

Mathematics

Differential Geometry

10 pages, 0 figures, preprint

Scientific paper

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.

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