Arnold‐Thom Gradient Conjecture for the Arrival Time
Author(s)Colding, Tobias; Minicozzi, William
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We prove conjectures of René 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications on Pure and Applied Mathematics
Colding, Tobias Holck and William P. Minicozzi II. "Arnold‐Thom Gradient Conjecture for the Arrival Time." Communications on Pure and Applied Mathematics Volume 72 (2019) © 2019 The Author(s)
Applied Mathematics, General Mathematics