Arnold‐Thom Gradient Conjecture for the Arrival Time

Arnold‐Thom Gradient Conjecture for the Arrival Time

We prove conjectures of René 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 ar...

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Veröffentlicht in:Communications on pure and applied mathematics 2019-07, Vol.72 (7), p.1548-1577
Hauptverfasser: Colding, Tobias Holck, Minicozzi, William P.
Format: Artikel
Sprache:eng
Schlagworte:
Curvature
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Zusammenfassung:We prove conjectures of René 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. © 2019 Wiley Periodicals, Inc.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21824