Curvatures of embedded minimal disks blow up on subsets of C^1 curves

Details Curvatures of embedded minimal disks blow up on subsets of C^1 curves Curvatures of embedded minimal disks blow up on subsets of C^1 curves

2011-03-29

arxiv.org/abs/1103.5551v2

Mathematics

Differential Geometry

6 pages. Minor revisions to previous version

Scientific paper

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.

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