Arnold-Thom gradient conjecture for the arrival time
Differential Geometry
2017-12-15 v1 Algebraic Geometry
Analysis of PDEs
Abstract
We prove conjectures of Rene Thom and Vladimir Arnold for C^2 solutions to the degenerate elliptic equation that is the level set equation for motion by mean curvature. We believe these results are the first instances of a general principle: Solutions of many degenerate equations behave as if they are analytic, even when they are not. If so, this would explain various conjectured phenomena.
Keywords
Cite
@article{arxiv.1712.05381,
title = {Arnold-Thom gradient conjecture for the arrival time},
author = {Tobias Holck Colding and William P. Minicozzi},
journal= {arXiv preprint arXiv:1712.05381},
year = {2017}
}