Regularity of the singular set in the Colding-Minicozzi lamination theorem (Q701892)

It is proved that the singular set \(S({\mathcal L})\) of convergence in the Colding-Minicozzi limit lamination theorem is a \(C^{1,1}\)-curve which is orthogonal to the limit minimal foliation \({\mathcal L}\) in some neighbourhood of \(S({\mathcal L})\).