Arnold‐Thom Gradient Conjecture for the Arrival Time
Name
1712.05381.pdf
Description
Submitted version
Size
541.68 KB
Format
Adobe PDF
Checksum (MD5)
edcccd45113cfe66fde230285ba6c625
Author(s)
Colding, Tobias
Minicozzi, William
Date Issued
March 13, 2019
Journal
Communications on Pure and Applied Mathematics
Publisher
Wiley
Citation
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)
Version
Original manuscript
Abstract
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.
Subjects
Applied Mathematics
General Mathematics
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1002/cpa.21824
