Arnold-Thom gradient conjecture for the arrival time
Abstract
We prove conjectures of Rene Thom and Vladimir Arnold for C2 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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