{"paper":{"title":"Complete translating solitons to the mean curvature flow in $\\mathbb{R}^3$ with nonnegative mean curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Joel Spruck, Ling Xiao","submitted_at":"2017-03-03T00:34:02Z","abstract_excerpt":"We prove that any complete immersed two-sided mean convex translating soliton $\\Sigma \\subset \\mathbb{R}^3$ for the mean curvature flow is convex. As a corollary it follows that an entire mean convex graphical translating soliton in $\\mathbb{R}^3$ is the axisymmetric \"bowl soliton\". We also show that if the mean curvature of $\\Sigma$ tends to zero at infinity, then $\\Sigma$ can be represented as an entire graph and so is the \"bowl soliton\". Finally we classify all locally strictly convex graphical translating solitons defined over strip regions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01003","kind":"arxiv","version":3},"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"}