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arXiv · 1712.05381

Arnold-Thom gradient conjecture for the arrival time

Tobias Holck Colding·William P. Minicozzi II
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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.

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Tobias Holck Colding, William P. Minicozzi II. 2017-12-14. Arnold-Thom gradient conjecture for the arrival time. https://arxiv.org/abs/1712.05381

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