Regularity of elliptic and parabolic systems
Differential Geometry
2020-02-17 v3 Analysis of PDEs
Abstract
We show uniqueness of cylindrical blowups for mean curvature flow in all dimension and all codimension. Cylindrical singularities are known to be the most important; they are the most prevalent in any codimension. Mean curvature flow in higher codimension is a nonlinear parabolic system where many of the methods used for hypersurfaces do not apply and uniqueness of cylindrical blowups remained a major open problem. Our results imply regularity of the singular set for the system.
Keywords
Cite
@article{arxiv.1905.00085,
title = {Regularity of elliptic and parabolic systems},
author = {Tobias Holck Colding and William P. Minicozzi},
journal= {arXiv preprint arXiv:1905.00085},
year = {2020}
}