{"paper":{"title":"Arnold-Thom gradient conjecture for the arrival time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AP"],"primary_cat":"math.DG","authors_text":"Tobias Holck Colding, William P. Minicozzi II","submitted_at":"2017-12-14T18:28:50Z","abstract_excerpt":"We prove conjectures of Rene Thom and Vladimir Arnold for C^2 solutions to the degenerate elliptic equation that is the level set equation for motion by mean curvature.\n  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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05381","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}