{"paper":{"title":"Convergence of Curve Shortening Flow to Translating Soliton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Beomjun Choi, Kyeongsu Choi, Panagiota Daskalopoulos","submitted_at":"2018-07-29T19:25:58Z","abstract_excerpt":"This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in $\\mathbb{R}^2$ under the $\\alpha$-curve shortening flow for exponents $\\alpha >\\frac12$. We show that any such curve having in addition its two ends asymptotic to two parallel lines, converges under $\\alpha$-curve shortening flow to the unique translating soliton whose ends are asymptotic to the same parallel lines. This is a new result even in the standard case $\\alpha=1$, and we prove for all exponents up to the critical case $\\alpha>\\frac12$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11100","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"}