We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is -close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singular set, and will have a unique tangent flow.
"Universality in mean curvature flow neckpinches." Duke Math. J. 164 (12) 2341 - 2406, 15 September 2015. https://doi.org/10.1215/00127094-3146175