Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom