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Arnold‐Thom Gradient Conjecture for the Arrival Time
Author(s) -
Colding Tobias Holck,
Minicozzi William P.
Publication year - 2019
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21824
Subject(s) - degenerate energy levels , mathematics , conjecture , motion (physics) , curvature , mathematical analysis , mathematical physics , pure mathematics , geometry , classical mechanics , physics , quantum mechanics
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. © 2019 Wiley Periodicals, Inc.