Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow
Differential Geometry
2013-11-19 v2 Analysis of PDEs
Abstract
We study surfaces evolving by mean curvature flow (MCF). For an open set of initial data that are -close to round, but without assuming rotational symmetry or positive mean curvature, we show that MCF solutions become singular in finite time by forming neckpinches, and we obtain detailed asymptotics of that singularity formation. Our results show in a precise way that MCF solutions become asymptotically rotationally symmetric near a neckpinch singularity.
Keywords
Cite
@article{arxiv.1109.0939,
title = {Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow},
author = {Zhou Gang and Dan Knopf and Israel Michael Sigal},
journal= {arXiv preprint arXiv:1109.0939},
year = {2013}
}
Comments
This revision corrects minor but potentially confusing misprints in Section 3