Regularity of the level set flow
Differential Geometry
2016-06-17 v1 Analysis of PDEs
Abstract
We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative. We show here that the second derivative is continuous if and only if the flow has a single singular time where it becomes extinct and the singular set consists of a closed manifold with cylindrical singularities.
Keywords
Cite
@article{arxiv.1606.05185,
title = {Regularity of the level set flow},
author = {Tobias Holck Colding and William P. Minicozzi},
journal= {arXiv preprint arXiv:1606.05185},
year = {2016}
}