  Any sequence of properly embedded minimal disks in an open subset U of
Euclidean 3-space has a subsequence such that the curvatures blow up on a
relatively closed subset K of U and such that the disks converge in the
complement of K to a minimal lamination of U\K. Assuming results of
Colding-Minicozzi and an extension due to Meeks, we prove that such a blow-up
set K must be contained in a C^1 embedded curve.
